// Numbas version: exam_results_page_options
{"percentPass": "40", "timing": {"timeout": {"action": "none", "message": ""}, "allowPause": false, "timedwarning": {"action": "none", "message": ""}}, "name": "Random Knowledge Test", "showQuestionGroupNames": false, "duration": 10800, "navigation": {"allowregen": false, "showresultspage": "oncompletion", "showfrontpage": true, "reverse": true, "onleave": {"action": "none", "message": ""}, "browse": true, "preventleave": true}, "question_groups": [{"pickQuestions": "12", "name": "Group", "pickingStrategy": "random-subset", "questions": [{"name": "2014-3", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Swa Lup", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2902/"}], "ungrouped_variables": ["npva", "v", "int", "amount1", "amount2", "amount3", "bAns", "d", "amount4", "An"], "variablesTest": {"maxRuns": 100, "condition": ""}, "parts": [{"variableReplacementStrategy": "originalfirst", "sortAnswers": false, "prompt": "<p>Find the net present value of Project A at an effective annual interest rate of 10%.</p>\n<p>NPVa :&nbsp;&pound;[[0]] in million</p>", "type": "gapfill", "scripts": {}, "marks": 0, "extendBaseMarkingAlgorithm": true, "gaps": [{"variableReplacementStrategy": "originalfirst", "type": "numberentry", "scripts": {}, "showCorrectAnswer": true, "allowFractions": false, "maxValue": "{npva}*1000000+5", "marks": 1, "extendBaseMarkingAlgorithm": true, "correctAnswerFraction": false, "minValue": "{npva}*1000000-5", "showFeedbackIcon": true, "customMarkingAlgorithm": "", "mustBeReducedPC": 0, "mustBeReduced": false, "correctAnswerStyle": "plain", "notationStyles": ["plain", "en", "si-en"], "unitTests": [], "variableReplacements": []}], "showFeedbackIcon": true, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "unitTests": [], "variableReplacements": []}, {"variableReplacementStrategy": "originalfirst", "sortAnswers": false, "prompt": "<p>Find the value of X if both projects are to have the same net present value at an interest rate of 10% per annum.&nbsp;</p>\n<p>X:&nbsp;&pound;[[0]]</p>", "type": "gapfill", "scripts": {}, "marks": 0, "extendBaseMarkingAlgorithm": true, "gaps": [{"variableReplacementStrategy": "originalfirst", "type": "numberentry", "scripts": {}, "showCorrectAnswer": true, "allowFractions": false, "maxValue": "{bAns}*1000000+5", "marks": 1, "extendBaseMarkingAlgorithm": true, "correctAnswerFraction": false, "minValue": "{bAns}*1000000-5", "showFeedbackIcon": true, "customMarkingAlgorithm": "", "mustBeReducedPC": 0, "mustBeReduced": false, "correctAnswerStyle": "plain", "notationStyles": ["plain", "en", "si-en"], "unitTests": [], "variableReplacements": []}], "showFeedbackIcon": true, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "unitTests": [], "variableReplacements": []}], "variable_groups": [], "metadata": {"licence": "None specified", "description": ""}, "tags": [], "statement": "<p>A company is considering two investment projects. Project A requires an immediate expenditure of &pound;2 million and &pound;4 million at time 2. In return a sum of &pound;900,000 per annum is paid continuously from time 5 to time 25. Project B requires regular payments of &pound;100,000 at the start of each year for 10 years. In return, amounts of X,2X,3X and so on are made annually for 10 years, the \ufb01rst payment being made at time 11</p>", "rulesets": {}, "advice": "", "variables": {"int": {"name": "int", "group": "Ungrouped variables", "definition": "random(10..10#1)", "templateType": "randrange", "description": ""}, "amount3": {"name": "amount3", "group": "Ungrouped variables", "definition": "random(0.9..0.9#1)", "templateType": "randrange", "description": ""}, "amount1": {"name": "amount1", "group": "Ungrouped variables", "definition": "random(2..2#1)", "templateType": "randrange", "description": ""}, "amount2": {"name": "amount2", "group": "Ungrouped variables", "definition": "random(4..4#1)", "templateType": "randrange", "description": ""}, "npva": {"name": "npva", "group": "Ungrouped variables", "definition": "(-{amount1}-{amount2}*({v}^2)+{amount3}*({v}^5)((1-{v}^20))/ln(1+{int}/100))\n", "templateType": "anything", "description": ""}, "amount4": {"name": "amount4", "group": "Ungrouped variables", "definition": "random(0.1..0.1#1)", "templateType": "randrange", "description": ""}, "An": {"name": "An", "group": "Ungrouped variables", "definition": "((1-{v}^10)/{d})", "templateType": "anything", "description": ""}, "v": {"name": "v", "group": "Ungrouped variables", "definition": "1/(1+{int}/100)", "templateType": "anything", "description": ""}, "bAns": {"name": "bAns", "group": "Ungrouped variables", "definition": "(-{amount4}*{an}-{npva})/-((({an}-10{v}^10)/({int}/100))*{v}^10)", "templateType": "anything", "description": "<p>b Answer</p>"}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "({int}/100)/(1+{int}/100)", "templateType": "anything", "description": ""}}, "preamble": {"css": "", "js": ""}, "functions": {}, "type": "question"}, {"name": "2014-1a", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Swa Lup", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2902/"}], "variables": {"int": {"templateType": "randrange", "definition": "random(6..6#1)", "group": "Ungrouped variables", "name": "int", "description": ""}, "d": {"templateType": "anything", "definition": "{iford}/(1+{iford})", "group": "Ungrouped variables", "name": "d", "description": ""}, "d12": {"templateType": "anything", "definition": "(1-(1-{d})^(1/12))*12*100", "group": "Ungrouped variables", "name": "d12", "description": ""}, "i1": {"templateType": "anything", "definition": "{dfori}/(1-{dfori})", "group": "Ungrouped variables", "name": "i1", "description": ""}, "dfori": {"templateType": "anything", "definition": "1-(1-({int}/100)/4)^4", "group": "Ungrouped variables", "name": "dfori", "description": ""}, "i12": {"templateType": "anything", "definition": "((1+{i1})^(1/12)-1)*12*100", "group": "Ungrouped variables", "name": "i12", "description": ""}, "iford": {"templateType": "anything", "definition": "e^({int}/100)-1", "group": "Ungrouped variables", "name": "iford", "description": ""}}, "ungrouped_variables": ["int", "iford", "d", "d12", "dfori", "i1", "i12"], "advice": "", "functions": {}, "variablesTest": {"maxRuns": 100, "condition": ""}, "rulesets": {}, "metadata": {"licence": "None specified", "description": ""}, "variable_groups": [], "tags": [], "statement": "", "parts": [{"showCorrectAnswer": true, "gaps": [{"allowFractions": false, "showCorrectAnswer": true, "minValue": "{d12}-0.02", "notationStyles": ["plain", "en", "si-en"], "customMarkingAlgorithm": "", "mustBeReducedPC": 0, "scripts": {}, "maxValue": "{d12}+0.02", "mustBeReduced": false, "marks": 1, "unitTests": [], "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "correctAnswerFraction": false, "showFeedbackIcon": true, "type": "numberentry"}], "customMarkingAlgorithm": "", "scripts": {}, "sortAnswers": false, "variableReplacements": [], "unitTests": [], "marks": 0, "extendBaseMarkingAlgorithm": true, "prompt": "<p>If &delta; = {int}%, \ufb01nd d<sup>(12)</sup>.&nbsp;</p>\n<p>[[0]]%</p>", "variableReplacementStrategy": "originalfirst", "type": "gapfill", "showFeedbackIcon": true}, {"showCorrectAnswer": true, "gaps": [{"allowFractions": false, "showCorrectAnswer": true, "minValue": "{i12}-0.02", "notationStyles": ["plain", "en", "si-en"], "customMarkingAlgorithm": "", "mustBeReducedPC": 0, "scripts": {}, "maxValue": "{i12}+0.02", "mustBeReduced": false, "marks": 1, "unitTests": [], "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "correctAnswerFraction": false, "showFeedbackIcon": true, "type": "numberentry"}], "customMarkingAlgorithm": "", "scripts": {}, "sortAnswers": false, "variableReplacements": [], "unitTests": [], "marks": 0, "extendBaseMarkingAlgorithm": true, "prompt": "<p>If d<sup>(4)</sup> = {int}%, \ufb01nd <em>i</em><sup>(12)</sup>.</p>\n<p>[[0]]%</p>", "variableReplacementStrategy": "originalfirst", "type": "gapfill", "showFeedbackIcon": true}], "preamble": {"js": "", "css": ""}, "type": "question"}, {"name": "2015-1a", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Swa Lup", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2902/"}], "preamble": {"js": "", "css": ""}, "statement": "", "ungrouped_variables": ["int", "d", "interest", "i4", "nominal"], "variables": {"d": {"description": "", "group": "Ungrouped variables", "definition": "1-(1-({int}/100)/12)^12", "name": "d", "templateType": "anything"}, "i4": {"description": "", "group": "Ungrouped variables", "definition": "(((1+{interest})^(1/4))-1)*4", "name": "i4", "templateType": "anything"}, "interest": {"description": "", "group": "Ungrouped variables", "definition": "{d}/(1-{d})", "name": "interest", "templateType": "anything"}, "int": {"description": "", "group": "Ungrouped variables", "definition": "random(5..9#1)", "name": "int", "templateType": "randrange"}, "nominal": {"description": "", "group": "Ungrouped variables", "definition": "{i4}*100", "name": "nominal", "templateType": "anything"}}, "variable_groups": [], "functions": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "", "rulesets": {}, "parts": [{"type": "gapfill", "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "gaps": [{"type": "numberentry", "variableReplacementStrategy": "originalfirst", "allowFractions": false, "extendBaseMarkingAlgorithm": true, "correctAnswerStyle": "plain", "customMarkingAlgorithm": "", "unitTests": [], "minValue": "{nominal}-0.2", "variableReplacements": [], "marks": 1, "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "mustBeReduced": false, "maxValue": "{nominal}+0.2", "scripts": {}, "showCorrectAnswer": true, "showFeedbackIcon": true, "correctAnswerFraction": false}], "unitTests": [], "showCorrectAnswer": true, "variableReplacements": [], "marks": 0, "extendBaseMarkingAlgorithm": true, "prompt": "<p>Find the nominal interest rate convertible quarterly which is equivalent to a nominal discount rate of {int}% per annum convertible monthly.&nbsp;</p>\n<p>Interest rate Convertible quarterly: [[0]]%</p>", "sortAnswers": false, "scripts": {}, "showFeedbackIcon": true}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "type": "question"}, {"name": "2015-1b", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Swa Lup", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2902/"}], "variable_groups": [], "parts": [{"gaps": [{"correctAnswerFraction": false, "unitTests": [], "minValue": "{a1}-0.1", "showCorrectAnswer": true, "showFeedbackIcon": true, "allowFractions": false, "marks": 1, "variableReplacements": [], "correctAnswerStyle": "plain", "type": "numberentry", "mustBeReduced": false, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "maxValue": "{a1}+0.1", "mustBeReducedPC": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst"}, {"correctAnswerFraction": false, "unitTests": [], "minValue": "{a2}-0.1", "showCorrectAnswer": true, "showFeedbackIcon": true, "allowFractions": false, "marks": 1, "variableReplacements": [], "correctAnswerStyle": "plain", "type": "numberentry", "mustBeReduced": false, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "maxValue": "{a2}+0.1", "mustBeReducedPC": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst"}, {"correctAnswerFraction": false, "unitTests": [], "minValue": "{a3}-0.1", "showCorrectAnswer": true, "showFeedbackIcon": true, "allowFractions": false, "marks": 1, "variableReplacements": [], "correctAnswerStyle": "plain", "type": "numberentry", "mustBeReduced": false, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "maxValue": "{a3}+0.1", "mustBeReducedPC": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst"}], "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "unitTests": [], "type": "gapfill", "variableReplacements": [], "prompt": "<p>Determine the amount to which the initial &pound;1,000 will accumulate at the end of each of the three years.&nbsp;</p>\n<p>First Year:&nbsp;&pound;[[0]],</p>\n<p>Second Year:&nbsp;&pound;[[1]],</p>\n<p>Third Year:&nbsp;&pound;[[2]].</p>", "scripts": {}, "variableReplacementStrategy": "originalfirst", "sortAnswers": false, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true}], "preamble": {"css": "", "js": ""}, "advice": "", "variables": {"a2": {"templateType": "anything", "group": "Ungrouped variables", "name": "a2", "description": "", "definition": "{a1}*(1-({int1}/100)/4)^(-4)"}, "a1": {"templateType": "anything", "group": "Ungrouped variables", "name": "a1", "description": "", "definition": "1000*(1+({int}/100)/12)^12"}, "a3": {"templateType": "anything", "group": "Ungrouped variables", "name": "a3", "description": "", "definition": "{a2}*e^(0.1)"}, "int1": {"templateType": "randrange", "group": "Ungrouped variables", "name": "int1", "description": "", "definition": "random(6..8#1)"}, "int": {"templateType": "randrange", "group": "Ungrouped variables", "name": "int", "description": "", "definition": "random(4..6#1)"}}, "statement": "<p>&nbsp;The amount of &pound;1,000 is paid into a savings account on which interest is earned as follows:</p>\n<p>During the \ufb01rst year, interest is earned at a nominal rate of interest of {int}% per annum convertible monthly;</p>\n<p>during the second year, interest is earned at a nominal rate of discount of {int1}% per annum convertible quarterly;</p>\n<p>during the third year, interest is earned at a force of interest &delta;(t) per annum at time t where &delta;(t) = 0.04t for 2 &lt; t &lt; 3.&nbsp;</p>", "ungrouped_variables": ["a1", "a2", "a3", "int", "int1"], "rulesets": {}, "tags": [], "functions": {}, "variablesTest": {"maxRuns": 100, "condition": ""}, "metadata": {"licence": "None specified", "description": ""}, "type": "question"}, {"name": "2015-2a", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Swa Lup", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2902/"}], "preamble": {"css": "", "js": ""}, "variables": {"i1": {"group": "Ungrouped variables", "name": "i1", "description": "", "templateType": "number", "definition": "0.08"}, "i2": {"group": "Ungrouped variables", "name": "i2", "description": "", "templateType": "number", "definition": "0.09"}, "irr": {"group": "Ungrouped variables", "name": "irr", "description": "", "templateType": "anything", "definition": "({i1}+(0-{npv1})(({i2}-{i1})/({npv2}-{npv1})))*100"}, "npv1": {"group": "Ungrouped variables", "name": "npv1", "description": "", "templateType": "anything", "definition": "-500-200/(1+{i1})^2+1000/(1+{i1})^5"}, "npv2": {"group": "Ungrouped variables", "name": "npv2", "description": "", "templateType": "anything", "definition": "-500-200/(1+{i2})^2+1000/(1+{i2})^5"}}, "tags": [], "statement": "<p>In return for an immediate payment of &pound;500 and a further payment of &pound;200 two years from now, aninvestor will receive &pound;1,000 after 5 years.</p>\n<p></p>", "parts": [{"marks": 0, "showCorrectAnswer": true, "type": "gapfill", "showFeedbackIcon": true, "gaps": [{"correctAnswerStyle": "plain", "marks": 1, "showCorrectAnswer": true, "type": "numberentry", "showFeedbackIcon": true, "allowFractions": false, "mustBeReduced": false, "minValue": "{irr}-0.5", "mustBeReducedPC": 0, "variableReplacements": [], "unitTests": [], "maxValue": "{irr}+0.5", "extendBaseMarkingAlgorithm": true, "correctAnswerFraction": false, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst"}], "variableReplacements": [], "prompt": "<p>Calculatethe internal rate of return(IRR)of the transaction using the linear interpolation method.&nbsp;</p>\n<p>IRR: [[0]] %</p>", "unitTests": [], "extendBaseMarkingAlgorithm": true, "scripts": {}, "sortAnswers": false, "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst"}], "metadata": {"licence": "All rights reserved", "description": ""}, "functions": {}, "rulesets": {}, "advice": "", "variablesTest": {"condition": "", "maxRuns": 100}, "variable_groups": [], "ungrouped_variables": ["irr", "i1", "i2", "npv1", "npv2"], "type": "question"}, {"name": "2015-2b", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Swa Lup", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2902/"}], "preamble": {"js": "", "css": ""}, "statement": "<p>A company wants to invest &pound;30 million into a new project that costs &pound;50 million. The company proposes to borrow the remaining &pound;20 million for the project at a force of interest of {force}% per annum. Repayments can be made in part or in whole at any time, and positive cash balances can be invested to yield {int}% per annum. The project will produce an income of &pound;8 million per annum, payable continuously for the next 5 years. Furthermore, the investor expects to receive a \ufb01nal income of &pound;25 million at the end of year 5.&nbsp;</p>", "ungrouped_variables": ["force", "int", "Dpp", "Profit", "sn"], "variables": {"sn": {"description": "", "group": "Ungrouped variables", "definition": "((1+{int}/100)^(5-{dpp})-1)/(ln(1+{int}/100))", "name": "sn", "templateType": "anything"}, "Dpp": {"description": "", "group": "Ungrouped variables", "definition": "ln(1-(20/8)*({force}/100))/(-{force}/100)", "name": "Dpp", "templateType": "anything"}, "force": {"description": "", "group": "Ungrouped variables", "definition": "random(4..8#1)", "name": "force", "templateType": "randrange"}, "int": {"description": "", "group": "Ungrouped variables", "definition": "random(4..6#1)", "name": "int", "templateType": "randrange"}, "Profit": {"description": "", "group": "Ungrouped variables", "definition": "25+8{sn}-30(1+{int}/100)^5", "name": "Profit", "templateType": "anything"}}, "variable_groups": [], "functions": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "", "rulesets": {}, "parts": [{"type": "gapfill", "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "gaps": [{"type": "numberentry", "variableReplacementStrategy": "originalfirst", "allowFractions": false, "extendBaseMarkingAlgorithm": true, "correctAnswerStyle": "plain", "customMarkingAlgorithm": "", "unitTests": [], "minValue": "{dpp}-0.3", "variableReplacements": [], "marks": 1, "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "mustBeReduced": false, "maxValue": "{dpp}+0.3", "scripts": {}, "showCorrectAnswer": true, "showFeedbackIcon": true, "correctAnswerFraction": false}], "unitTests": [], "showCorrectAnswer": true, "variableReplacements": [], "marks": 0, "extendBaseMarkingAlgorithm": true, "prompt": "<p>Find the discounted payback period (DPP) for the &pound;20 million loan if the company is using all pro\ufb01ts associated with this project to repay the loan as soon as possible</p>\n<p>Discounted Payback Period: [[0]] Years.</p>", "sortAnswers": false, "scripts": {}, "showFeedbackIcon": true}, {"type": "gapfill", "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "gaps": [{"type": "numberentry", "variableReplacementStrategy": "originalfirst", "allowFractions": false, "extendBaseMarkingAlgorithm": true, "correctAnswerStyle": "plain", "customMarkingAlgorithm": "", "unitTests": [], "minValue": "{profit}-0.5", "variableReplacements": [], "marks": 1, "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "mustBeReduced": false, "maxValue": "{profit}+0.5", "scripts": {}, "showCorrectAnswer": true, "showFeedbackIcon": true, "correctAnswerFraction": false}], "unitTests": [], "showCorrectAnswer": true, "variableReplacements": [], "marks": 0, "extendBaseMarkingAlgorithm": true, "prompt": "<p>&nbsp;Find the accumulated pro\ufb01t of the investment.</p>\n<p>Profit: &pound;[[0]] Millions</p>", "sortAnswers": false, "scripts": {}, "showFeedbackIcon": true}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "type": "question"}, {"name": "2015-3a", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Swa Lup", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2902/"}], "preamble": {"js": "", "css": ""}, "statement": "<p>You plan to accumulate &pound;100,000 at the end of 42 years by making the following deposits:</p>\n<p>X at the beginning of years 1 to 14;</p>\n<p>No deposits at the beginning of years 15 to 32;</p>\n<p>and Y at the beginning of years 33 to 42.</p>\n<p>The annual effective interest rate is {int}%.</p>", "ungrouped_variables": ["int", "Sna", "d", "y"], "variables": {"y": {"description": "", "group": "Ungrouped variables", "definition": "(100000-{sna}*100)/({sna}+(((1+{int}/100)^10-1)/{d}))", "name": "y", "templateType": "anything"}, "Sna": {"description": "", "group": "Ungrouped variables", "definition": "(1+{int}/100)^28*(((1+{int}/100)^14-1)/{d})", "name": "Sna", "templateType": "anything"}, "int": {"description": "", "group": "Ungrouped variables", "definition": "random(6..8#1)", "name": "int", "templateType": "randrange"}, "d": {"description": "", "group": "Ungrouped variables", "definition": "({int}/100)/(1+{int}/100)", "name": "d", "templateType": "anything"}}, "variable_groups": [], "metadata": {"description": "", "licence": "None specified"}, "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "", "rulesets": {}, "parts": [{"variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "unitTests": [], "showCorrectAnswer": true, "variableReplacements": [], "marks": 0, "gaps": [{"type": "numberentry", "scripts": {}, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "minValue": "{y}-30", "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "unitTests": [], "showCorrectAnswer": true, "variableReplacements": [], "maxValue": "{y}+30", "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "correctAnswerFraction": false, "marks": 1, "correctAnswerStyle": "plain", "showFeedbackIcon": true, "mustBeReduced": false}], "prompt": "<p>If X &minus;Y = 100, calculate Y.</p>\n<p>Y: &pound;[[0]]</p>", "sortAnswers": false, "scripts": {}, "type": "gapfill"}], "tags": [], "functions": {}, "type": "question"}, {"name": "2015-3a", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Swa Lup", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2902/"}], "preamble": {"js": "", "css": ""}, "statement": "<p>You plan to accumulate &pound;100,000 at the end of 42 years by making the following deposits:</p>\n<p>X at the beginning of years 1 to 14;</p>\n<p>No deposits at the beginning of years 15 to 32;</p>\n<p>and Y at the beginning of years 33 to 42.</p>\n<p>The annual effective interest rate is {int}%.</p>", "ungrouped_variables": ["int", "Sna", "d", "y"], "variables": {"y": {"description": "", "group": "Ungrouped variables", "definition": "(100000-{sna}*100)/({sna}+(((1+{int}/100)^10-1)/{d}))", "name": "y", "templateType": "anything"}, "Sna": {"description": "", "group": "Ungrouped variables", "definition": "(1+{int}/100)^28*(((1+{int}/100)^14-1)/{d})", "name": "Sna", "templateType": "anything"}, "int": {"description": "", "group": "Ungrouped variables", "definition": "random(6..8#1)", "name": "int", "templateType": "randrange"}, "d": {"description": "", "group": "Ungrouped variables", "definition": "({int}/100)/(1+{int}/100)", "name": "d", "templateType": "anything"}}, "variable_groups": [], "metadata": {"description": "", "licence": "None specified"}, "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "", "rulesets": {}, "parts": [{"variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "unitTests": [], "showCorrectAnswer": true, "variableReplacements": [], "marks": 0, "gaps": [{"type": "numberentry", "scripts": {}, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "minValue": "{y}-30", "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "unitTests": [], "showCorrectAnswer": true, "variableReplacements": [], "maxValue": "{y}+30", "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "correctAnswerFraction": false, "marks": 1, "correctAnswerStyle": "plain", "showFeedbackIcon": true, "mustBeReduced": false}], "prompt": "<p>If X &minus;Y = 100, calculate Y.</p>\n<p>Y: &pound;[[0]]</p>", "sortAnswers": false, "scripts": {}, "type": "gapfill"}], "tags": [], "functions": {}, "type": "question"}, {"name": "2015-3b", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Swa Lup", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2902/"}], "ungrouped_variables": ["payment", "repayment", "money", "money1", "int", "v", "lhs", "d12"], "variablesTest": {"condition": "", "maxRuns": 100}, "parts": [{"variableReplacementStrategy": "originalfirst", "sortAnswers": false, "prompt": "<p>Find the appropriate single payment if option 1 is accepted by the bank.</p>\n<p>Payment:&nbsp;&pound;[[0]]</p>", "type": "gapfill", "scripts": {}, "marks": 0, "extendBaseMarkingAlgorithm": true, "gaps": [{"marks": 1, "type": "numberentry", "scripts": {}, "correctAnswerFraction": false, "allowFractions": false, "maxValue": "{payment}+15", "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "correctAnswerStyle": "plain", "minValue": "{payment}-15", "showFeedbackIcon": true, "customMarkingAlgorithm": "", "mustBeReducedPC": 0, "mustBeReduced": false, "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "unitTests": [], "variableReplacements": []}], "showFeedbackIcon": true, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "unitTests": [], "variableReplacements": []}, {"variableReplacementStrategy": "originalfirst", "sortAnswers": false, "prompt": "<p>Find the appropriate monthly repayment if option 2 is accepted.</p>\n<p>Repayment:&pound;[[0]]</p>", "type": "gapfill", "scripts": {}, "marks": 0, "extendBaseMarkingAlgorithm": true, "gaps": [{"marks": 1, "type": "numberentry", "scripts": {}, "correctAnswerFraction": false, "allowFractions": false, "maxValue": "{repayment}+2.5", "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "correctAnswerStyle": "plain", "minValue": "{repayment}-2.5", "showFeedbackIcon": true, "customMarkingAlgorithm": "", "mustBeReducedPC": 0, "mustBeReduced": false, "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "unitTests": [], "variableReplacements": []}], "showFeedbackIcon": true, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "unitTests": [], "variableReplacements": []}], "variable_groups": [], "metadata": {"licence": "None specified", "description": ""}, "tags": [], "statement": "<p>A borrower is under an obligation to repay a bank &pound;{money} in two years&rsquo; time and &pound;{money1} in three years&rsquo;time. As part of a review of his future commitments, the borrower now offers either</p>\n<p>option 1: to discharge his liability for these two debts by making an appropriate single payment two years from now;</p>\n<p>or option 2: to repay the total amount owed by making 24 appropriate equal payments made at one month&rsquo; intervals, the \ufb01rst payment being due now.</p>\n<p>The repayments are calculated using an effective rate of interest of {int}% per annum.&nbsp;</p>", "rulesets": {}, "advice": "", "variables": {"int": {"name": "int", "templateType": "randrange", "definition": "random(8..12#1)", "group": "Ungrouped variables", "description": ""}, "money": {"name": "money", "templateType": "randrange", "definition": "random(4000..4600#100)", "group": "Ungrouped variables", "description": ""}, "repayment": {"name": "repayment", "templateType": "anything", "definition": "{lhs}/(12*((1-{v}^2)/{d12}))", "group": "Ungrouped variables", "description": ""}, "money1": {"name": "money1", "templateType": "randrange", "definition": "random(1000..1400#100)", "group": "Ungrouped variables", "description": ""}, "lhs": {"name": "lhs", "templateType": "anything", "definition": "{money}*{v}^2+{money1}*{v}^3", "group": "Ungrouped variables", "description": "<p>left hand side</p>\n<p></p>"}, "payment": {"name": "payment", "templateType": "anything", "definition": "{lhs}/{v}^2", "group": "Ungrouped variables", "description": ""}, "d12": {"name": "d12", "templateType": "anything", "definition": "(1-(1-(({int}/100)*{v}))^(1/12))*12", "group": "Ungrouped variables", "description": ""}, "v": {"name": "v", "templateType": "anything", "definition": "1/(1+{int}/100)", "group": "Ungrouped variables", "description": ""}}, "preamble": {"css": "", "js": ""}, "functions": {}, "type": "question"}, {"name": "2015-4a", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Swa Lup", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2902/"}], "ungrouped_variables": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "functions": {}, "variable_groups": [], "metadata": {"licence": "None specified", "description": ""}, "tags": [], "statement": "<p>Consider a bond with face value <em>f</em>, redemption value C, current price<em> P</em> which has a coupon rate of r% payable <em>m</em> times per year for <em>n</em> years. Taxation is at the rate t1 and is paid at the end of each year, hence the annual tax is t<sub>1</sub><em>f</em><sub>r</sub>.&nbsp;Find an equation for the yield to maturity.&nbsp;</p>", "rulesets": {}, "advice": "", "preamble": {"css": "", "js": ""}, "parts": [{"marks": 0, "sortAnswers": false, "prompt": "<p>Find an equation for the yield to maturity.&nbsp;</p>\n<p>[[0]]</p>\n<p></p>\n<p></p>", "type": "gapfill", "scripts": {}, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "gaps": [{"distractors": ["", "", "", ""], "marks": 0, "type": "1_n_2", "scripts": {}, "choices": ["<math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\">$P = (1-t1)fr[{(1-{1 \\over&nbsp; (1+i)^n}) \\over i^m}]+C[{1 \\over (1+i)}]^n.$</math>", "<math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\">$P = (1-t1)fr[{(1-{1 \\over&nbsp; (1+i)^m}) \\over i^n}]+C[{1 \\over (1+i)}]^n.$</math>", "$P = (1-t1)fr[{(1-{1 \\over (1+i)^m}) \\over i^n}].$", "$P = (1-t1)fr[{(1-{1 \\over (1+i)^n}) \\over i^n}].$"], "displayColumns": 0, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "displayType": "radiogroup", "shuffleChoices": false, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "showCellAnswerState": true, "matrix": ["1", 0, 0, 0], "minMarks": 0, "showCorrectAnswer": true, "maxMarks": 0, "unitTests": [], "variableReplacements": []}], "showFeedbackIcon": true, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "unitTests": [], "variableReplacements": []}], "variables": {}, "type": "question"}, {"name": "2015-4b", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Swa Lup", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2902/"}], "variables": {"i22": {"templateType": "anything", "group": "Ungrouped variables", "definition": "((1+{int1}/100)^(1/2)-1)*2", "name": "i22", "description": ""}, "i2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "((1+{int}/100)^(1/2)-1)*2", "name": "i2", "description": ""}, "below": {"templateType": "anything", "group": "Ungrouped variables", "definition": "(1-({tax2}/100)*{v1}^(15-{year}))", "name": "below", "description": ""}, "tax1": {"templateType": "randrange", "group": "Ungrouped variables", "definition": "random(25..25#5)", "name": "tax1", "description": ""}, "tax2": {"templateType": "randrange", "group": "Ungrouped variables", "definition": "random(35..45#5)", "name": "tax2", "description": ""}, "price": {"templateType": "anything", "group": "Ungrouped variables", "definition": "(1-{tax}/100)*4((1-{v}^15)/{i2})+100{v}^15", "name": "price", "description": ""}, "int1": {"templateType": "randrange", "group": "Ungrouped variables", "definition": "random(5..7#1)", "name": "int1", "description": ""}, "v1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "1/(1+{int1}/100)", "name": "v1", "description": ""}, "price1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "((1-({tax1}/100))*4{a22}+100{v1}^(15-{year})-(({tax2}/100)*100)*{v1}^(15-{year}))/{below}", "name": "price1", "description": ""}, "a22": {"templateType": "anything", "group": "Ungrouped variables", "definition": "(1-{v1}^(15-{year}))/{i22}", "name": "a22", "description": ""}, "year": {"templateType": "randrange", "group": "Ungrouped variables", "definition": "random(7..9#1)", "name": "year", "description": ""}, "int": {"templateType": "randrange", "group": "Ungrouped variables", "definition": "random(4..7#1)", "name": "int", "description": ""}, "v": {"templateType": "anything", "group": "Ungrouped variables", "definition": "1/(1+{int}/100)", "name": "v", "description": ""}, "tax": {"templateType": "randrange", "group": "Ungrouped variables", "definition": "random(20..25#5)", "name": "tax", "description": ""}}, "ungrouped_variables": ["tax", "int", "price", "v", "i2", "price1", "tax1", "year", "tax2", "int1", "i22", "v1", "a22", "below"], "functions": {}, "advice": "", "statement": "<p>&nbsp;Investor A purchased a bond with exactly 15 years to redemption. The bond is redeemable at par and has a gross redemption yield of {int}% per annum effective. It pays coupons of 4% per annum, half-yearly in arrears. He pays tax at {tax}% on the coupons only</p>", "variablesTest": {"maxRuns": 100, "condition": ""}, "metadata": {"licence": "None specified", "description": ""}, "variable_groups": [], "preamble": {"js": "", "css": ""}, "tags": [], "rulesets": {}, "parts": [{"showCorrectAnswer": true, "gaps": [{"allowFractions": false, "maxValue": "{price}+5", "notationStyles": ["plain", "en", "si-en"], "customMarkingAlgorithm": "", "minValue": "{price}-5", "mustBeReducedPC": 0, "showCorrectAnswer": true, "mustBeReduced": false, "marks": 1, "unitTests": [], "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "scripts": {}, "variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "type": "numberentry", "showFeedbackIcon": true, "correctAnswerFraction": false}], "customMarkingAlgorithm": "", "scripts": {}, "sortAnswers": false, "variableReplacements": [], "unitTests": [], "marks": 0, "extendBaseMarkingAlgorithm": true, "prompt": "<p>Calculate the price paid by investor A for the bond.</p>\n<p><br/>Price paid: &pound;[[0]]</p>", "variableReplacementStrategy": "originalfirst", "type": "gapfill", "showFeedbackIcon": true}, {"showCorrectAnswer": true, "gaps": [{"allowFractions": false, "maxValue": "{price1}+5", "notationStyles": ["plain", "en", "si-en"], "customMarkingAlgorithm": "", "minValue": "{price1}-5", "mustBeReducedPC": 0, "showCorrectAnswer": true, "mustBeReduced": false, "marks": 1, "unitTests": [], "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "scripts": {}, "variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "type": "numberentry", "showFeedbackIcon": true, "correctAnswerFraction": false}], "customMarkingAlgorithm": "", "scripts": {}, "sortAnswers": false, "variableReplacements": [], "unitTests": [], "marks": 0, "extendBaseMarkingAlgorithm": true, "prompt": "<p>After exactly {year} years, immediately after the payment of the coupon then due, investor A sells this bond to investor B who pays income tax at a rate of {tax1}% and capital gains tax at a rate of {tax2}%. The bond is purchased by investor B to provide a net return of {int1}% per annum effective. Calculate the price paid by investor B.&nbsp;</p>\n<p></p>\n<p>Price paid: &pound;[[0]]</p>", "variableReplacementStrategy": "originalfirst", "type": "gapfill", "showFeedbackIcon": true}], "type": "question"}, {"name": "2015-5", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Swa Lup", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2902/"}], "variables": {"t": {"templateType": "anything", "group": "Ungrouped variables", "definition": "({year}+5{v}^3)/(1+2.5{v}^3)", "name": "t", "description": ""}, "payment1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "{payment}2.5", "name": "payment1", "description": ""}, "payment": {"templateType": "anything", "group": "Ungrouped variables", "definition": "(7107.77{year})/(({v}^{t})*({t}+7.5{v}^3+2.5{t}*{v}^3))", "name": "payment", "description": ""}, "year": {"templateType": "randrange", "group": "Ungrouped variables", "definition": "random(5..8#3)", "name": "year", "description": ""}, "t1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "{t}+3", "name": "t1", "description": ""}, "int": {"templateType": "randrange", "group": "Ungrouped variables", "definition": "random(8..8#1)", "name": "int", "description": ""}, "v": {"templateType": "anything", "group": "Ungrouped variables", "definition": "1/(1+{int}/100)", "name": "v", "description": ""}, "avt": {"templateType": "anything", "group": "Ungrouped variables", "definition": "7107.77/(1+2.5{v}^3)", "name": "avt", "description": ""}}, "ungrouped_variables": ["year", "int", "v", "avt", "t", "payment", "t1", "payment1"], "functions": {}, "advice": "", "statement": "<p>A fund has a liability to make two payments in the future, the \ufb01rst one due at the end of t years from now and the second one 3 years after the \ufb01rst. Further, the second payment is 2.5 times the \ufb01rst payment.</p>", "variablesTest": {"maxRuns": 100, "condition": ""}, "metadata": {"licence": "None specified", "description": ""}, "variable_groups": [], "preamble": {"js": "", "css": ""}, "tags": [], "rulesets": {}, "parts": [{"showCorrectAnswer": true, "gaps": [{"showCorrectAnswer": true, "displayType": "checkbox", "minMarks": 0, "distractors": ["", "", "", "", "", "", "", "", ""], "customMarkingAlgorithm": "", "scripts": {}, "marks": 0, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "type": "m_n_2", "warningType": "none", "showCellAnswerState": true, "maxMarks": 0, "choices": ["PV<sub>a&nbsp;</sub>= PV<sub>L</sub>", "PV<sub>a&nbsp;</sub>&lt;&nbsp;PV<sub>L</sub>", "PV<sub>a </sub>&gt;&nbsp;PV<sub>L</sub>", "D<sub>a&nbsp;</sub>= D<sub>L</sub>", "D<sub>a </sub>&lt; D<sub>L</sub>", "D<sub>a&nbsp;</sub>&gt;&nbsp;D<sub>L</sub>", "K<sub>a&nbsp;</sub>= K<sub>L</sub>", "K<sub>a&nbsp;</sub>&lt;&nbsp;K<sub>L</sub>", "K<sub>a&nbsp;</sub>&gt;&nbsp;K<sub>L</sub>"], "displayColumns": 0, "unitTests": [], "minAnswers": 0, "shuffleChoices": false, "matrix": ["1", 0, 0, "1", 0, 0, "0", 0, "1"], "showFeedbackIcon": true, "maxAnswers": 0}], "customMarkingAlgorithm": "", "scripts": {}, "sortAnswers": false, "variableReplacements": [], "unitTests": [], "marks": 0, "extendBaseMarkingAlgorithm": true, "prompt": "<p>State the Redington&rsquo;s conditions for immunisation of a portfolio of assets and liabilities against small changes in interest rates.&nbsp;</p>\n<p>[[0]]</p>", "variableReplacementStrategy": "originalfirst", "type": "gapfill", "showFeedbackIcon": true}, {"showCorrectAnswer": true, "gaps": [{"allowFractions": false, "maxValue": "{payment}+20", "notationStyles": ["plain", "en", "si-en"], "customMarkingAlgorithm": "", "minValue": "{payment}-20", "mustBeReducedPC": 0, "showCorrectAnswer": true, "mustBeReduced": false, "marks": 1, "unitTests": [], "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "scripts": {}, "variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "type": "numberentry", "showFeedbackIcon": true, "correctAnswerFraction": false}, {"allowFractions": false, "maxValue": "{payment1}+5", "notationStyles": ["plain", "en", "si-en"], "customMarkingAlgorithm": "", "minValue": "{payment1}-5", "mustBeReducedPC": 0, "showCorrectAnswer": true, "mustBeReduced": false, "marks": 1, "unitTests": [], "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "scripts": {}, "variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "type": "numberentry", "showFeedbackIcon": true, "correctAnswerFraction": false}, {"allowFractions": false, "showCorrectAnswer": true, "customMarkingAlgorithm": "", "mustBeReducedPC": 0, "maxValue": "{t}", "variableReplacements": [], "showPrecisionHint": true, "marks": 1, "extendBaseMarkingAlgorithm": true, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "type": "numberentry", "strictPrecision": true, "scripts": {}, "precisionPartialCredit": 0, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "unitTests": [], "minValue": "{t}", "precision": 0, "precisionMessage": "You have not given your answer to the correct precision.", "precisionType": "dp", "showFeedbackIcon": true}, {"allowFractions": false, "showCorrectAnswer": true, "customMarkingAlgorithm": "", "mustBeReducedPC": 0, "maxValue": "{t1}", "variableReplacements": [], "showPrecisionHint": true, "marks": 1, "extendBaseMarkingAlgorithm": true, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "type": "numberentry", "strictPrecision": true, "scripts": {}, "precisionPartialCredit": 0, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "unitTests": [], "minValue": "{t1}", "precision": 0, "precisionMessage": "You have not given your answer to the correct precision.", "precisionType": "dp", "showFeedbackIcon": true}], "customMarkingAlgorithm": "", "scripts": {}, "sortAnswers": false, "variableReplacements": [], "unitTests": [], "marks": 0, "extendBaseMarkingAlgorithm": true, "prompt": "<p>If the present value of these payments and discounted mean term of the liabilities at {int}% per annum effective are &pound;7,107.77 and {year} years respectively. Determine the timing (in complete years) and the amount of both payments.&nbsp;</p>\n<p>First payment:&nbsp;&pound;[[0]] in [[2]] years</p>\n<p>Second payment:&nbsp;&pound;[[1]] in [[3]] years</p>", "variableReplacementStrategy": "originalfirst", "type": "gapfill", "showFeedbackIcon": true}, {"showCorrectAnswer": true, "gaps": [{"showCorrectAnswer": true, "displayType": "radiogroup", "minMarks": 0, "distractors": ["", ""], "customMarkingAlgorithm": "", "choices": ["Yes, it is Satisfied", "No,&nbsp;it is not Satisfied"], "scripts": {}, "displayColumns": 0, "marks": 0, "unitTests": [], "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "shuffleChoices": false, "variableReplacementStrategy": "originalfirst", "maxMarks": 0, "type": "1_n_2", "showCellAnswerState": true, "showFeedbackIcon": true, "matrix": ["1", 0]}, {"showCorrectAnswer": true, "displayType": "radiogroup", "minMarks": 0, "distractors": ["", ""], "customMarkingAlgorithm": "", "choices": ["Yes, it is Satisfied", "No, it is not Satisfied"], "scripts": {}, "displayColumns": 0, "marks": 0, "unitTests": [], "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "shuffleChoices": false, "variableReplacementStrategy": "originalfirst", "maxMarks": 0, "type": "1_n_2", "showCellAnswerState": true, "showFeedbackIcon": true, "matrix": ["1", 0]}, {"showCorrectAnswer": true, "displayType": "radiogroup", "minMarks": 0, "distractors": ["", ""], "customMarkingAlgorithm": "", "choices": ["Yes,&nbsp;it is Satisfied", "No,&nbsp;it is not Satisfied"], "scripts": {}, "displayColumns": 0, "marks": 0, "unitTests": [], "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "shuffleChoices": false, "variableReplacementStrategy": "originalfirst", "maxMarks": 0, "type": "1_n_2", "showCellAnswerState": true, "showFeedbackIcon": true, "matrix": ["0", "1"]}], "customMarkingAlgorithm": "", "scripts": {}, "sortAnswers": false, "variableReplacements": [], "unitTests": [], "marks": 0, "extendBaseMarkingAlgorithm": true, "prompt": "<p>The asset backing this instrument is to be invested in a zero coupon bond maturing after 5 years giving maturity value of &pound;10,443.65. Investigate whether the fund satis\ufb01es the necessary conditions to be immunised against small interest changes in the rate of interest.&nbsp;</p>\n<p>Present Value: [[0]]</p>\n<p>Duration: [[1]]</p>\n<p>Convexity: [[2]]</p>", "variableReplacementStrategy": "originalfirst", "type": "gapfill", "showFeedbackIcon": true}], "type": "question"}, {"name": "2015-6a", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Swa Lup", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2902/"}], "variable_groups": [], "parts": [{"gaps": [{"correctAnswerFraction": false, "allowFractions": false, "showCorrectAnswer": true, "showFeedbackIcon": true, "unitTests": [], "marks": 1, "type": "numberentry", "variableReplacements": [], "correctAnswerStyle": "plain", "mustBeReduced": false, "minValue": "{price}-0.5", "scripts": {}, "variableReplacementStrategy": "originalfirst", "maxValue": "{price}+0.5", "mustBeReducedPC": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "notationStyles": ["plain", "en", "si-en"]}], "showCorrectAnswer": true, "showFeedbackIcon": true, "unitTests": [], "marks": 0, "type": "gapfill", "variableReplacements": [], "prompt": "<p>Assuming no arbitrage and that the share will not pay any income, calculate the forward price for the share, for settlement in exactly one quarter of a year.&nbsp;</p>\n<p>Forward price: &pound;[[0]]</p>", "scripts": {}, "variableReplacementStrategy": "originalfirst", "sortAnswers": false, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true}], "preamble": {"css": "", "js": ""}, "advice": "", "variables": {"pence": {"templateType": "randrange", "description": "", "name": "pence", "group": "Ungrouped variables", "definition": "random(0.6..0.8#0.1)"}, "int": {"templateType": "randrange", "description": "", "name": "int", "group": "Ungrouped variables", "definition": "random(4..7#1)"}, "price": {"templateType": "anything", "description": "", "name": "price", "group": "Ungrouped variables", "definition": "100*{pence}*(1+{int}/100)^(1/4)"}}, "statement": "<p>&nbsp;The price of a given share is {pence}p. The risk-free rate of interest is {int}% per annum convertible quarterly.</p>", "ungrouped_variables": ["price", "pence", "int"], "rulesets": {}, "tags": [], "functions": {}, "variablesTest": {"maxRuns": 100, "condition": ""}, "metadata": {"licence": "None specified", "description": ""}, "type": "question"}, {"name": "2015-6b", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Swa Lup", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2902/"}], "rulesets": {}, "tags": [], "variable_groups": [], "metadata": {"description": "", "licence": "None specified"}, "advice": "", "parts": [{"scripts": {}, "gaps": [{"scripts": {}, "type": "numberentry", "extendBaseMarkingAlgorithm": true, "marks": 1, "variableReplacementStrategy": "originalfirst", "unitTests": [], "mustBeReducedPC": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "allowFractions": false, "correctAnswerStyle": "plain", "correctAnswerFraction": false, "customMarkingAlgorithm": "", "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "maxValue": "{price}+5", "mustBeReduced": false, "minValue": "{price}-5"}], "type": "gapfill", "extendBaseMarkingAlgorithm": true, "marks": 0, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "unitTests": [], "showFeedbackIcon": true, "sortAnswers": false, "customMarkingAlgorithm": "", "variableReplacements": [], "prompt": "<p>&nbsp;Calculate the forward price at issue, assuming no arbitrage.</p>\n<p>Forward price:&nbsp;&pound;[[0]]</p>"}], "variables": {"int": {"definition": "random(4..6#1)", "group": "Ungrouped variables", "templateType": "randrange", "description": "", "name": "int"}, "price": {"definition": "(550-60((1+{int}/100)^(-1/2))-60((1+{int1}/100)^(-1)))/((1+{int1}/100)^(-1))", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "price"}, "int1": {"definition": "random(4.5..6.5#0.5)", "group": "Ungrouped variables", "templateType": "randrange", "description": "", "name": "int1"}}, "ungrouped_variables": ["int", "int1", "price"], "functions": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "statement": "<p>A one-year forward contract is issued on 1 January 2015 on a share with price of &pound;550 on that date. Dividends of &pound;60 are expected on 30 June 2015 and 31 December 2015. The risk-free spot rates for 6-month and 12-month are {int}% and {int1}% per annum effective respectively on 1 January 2015.</p>", "preamble": {"js": "", "css": ""}, "type": "question"}, {"name": "2015-7b", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Swa Lup", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2902/"}], "preamble": {"js": "", "css": ""}, "statement": "<p>&nbsp;An investor holds a short position in a forward contract on gold for delivery in 90 days at &pound;{spot} an ounce. The current spot price of gold is &pound;{spot1} an ounce. The insurance and storage cost for gold are {cost}% per annum of the spot price, paid on delivery. 90 days simple interest rates are {interest}% per annum.</p>", "ungrouped_variables": ["spot", "spot1", "cost", "interest", "price", "k"], "variables": {"spot1": {"description": "", "group": "Ungrouped variables", "definition": "{spot}-30", "name": "spot1", "templateType": "anything"}, "k": {"description": "", "group": "Ungrouped variables", "definition": "420(1+(90/365)*({interest}/100)+({cost}/100)*(90/365))", "name": "k", "templateType": "anything"}, "price": {"description": "", "group": "Ungrouped variables", "definition": "{spot}-{k}", "name": "price", "templateType": "anything"}, "spot": {"description": "", "group": "Ungrouped variables", "definition": "random(450..500#25)", "name": "spot", "templateType": "randrange"}, "interest": {"description": "", "group": "Ungrouped variables", "definition": "random(9..10#0.25)", "name": "interest", "templateType": "randrange"}, "cost": {"description": "", "group": "Ungrouped variables", "definition": "random(2..3#0.5)", "name": "cost", "templateType": "randrange"}}, "variable_groups": [], "functions": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "", "rulesets": {}, "parts": [{"type": "gapfill", "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "gaps": [{"type": "numberentry", "variableReplacementStrategy": "originalfirst", "allowFractions": false, "extendBaseMarkingAlgorithm": true, "correctAnswerStyle": "plain", "customMarkingAlgorithm": "", "unitTests": [], "minValue": "{price}-2.5", "variableReplacements": [], "marks": 1, "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "mustBeReduced": false, "maxValue": "{price}+2.5", "scripts": {}, "showCorrectAnswer": true, "showFeedbackIcon": true, "correctAnswerFraction": false}], "unitTests": [], "showCorrectAnswer": true, "variableReplacements": [], "marks": 0, "extendBaseMarkingAlgorithm": true, "prompt": "<p>What is the value of this forward contract?</p>\n<p>Value:&nbsp;&pound;[[0]]</p>", "sortAnswers": false, "scripts": {}, "showFeedbackIcon": true}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "type": "question"}, {"name": "2016-1a", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Swa Lup", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2902/"}], "preamble": {"css": "", "js": ""}, "variables": {"int1": {"group": "Ungrouped variables", "name": "int1", "description": "", "templateType": "randrange", "definition": "random(5..7#1)"}, "int2": {"group": "Ungrouped variables", "name": "int2", "description": "", "templateType": "anything", "definition": "{int1}-1"}, "years": {"group": "Ungrouped variables", "name": "years", "description": "", "templateType": "anything", "definition": "((({int1}/100)/ln(1+{int2}/100))-1)/({int1}/100)"}}, "tags": [], "statement": "<p>A fund accumulates at a simple interest rate of {int1}%. Another fund accumulates at a compound interest rate of {int2}% compounded once a year.&nbsp;</p>", "parts": [{"marks": 0, "showCorrectAnswer": true, "type": "gapfill", "showFeedbackIcon": true, "gaps": [{"correctAnswerStyle": "plain", "marks": 1, "showCorrectAnswer": true, "type": "numberentry", "showFeedbackIcon": true, "allowFractions": false, "mustBeReduced": false, "minValue": "{years}-0.2", "mustBeReducedPC": 0, "variableReplacements": [], "unitTests": [], "maxValue": "{years+0.2", "extendBaseMarkingAlgorithm": true, "correctAnswerFraction": false, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst"}, {"marks": 0, "showCorrectAnswer": true, "shuffleChoices": false, "distractors": ["", ""], "type": "1_n_2", "showFeedbackIcon": true, "displayColumns": 0, "matrix": [0, "1"], "showCellAnswerState": true, "choices": ["Simple interest rate", "Compounded interest rate"], "variableReplacements": [], "maxMarks": 0, "unitTests": [], "displayType": "radiogroup", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "scripts": {}, "customMarkingAlgorithm": "", "minMarks": 0}], "variableReplacements": [], "prompt": "<p>When will the force of interest be the same for the two funds? [[0]] Years</p>\n<p>After this point, which fund will have a higher force of interest? [[1]]</p>", "unitTests": [], "extendBaseMarkingAlgorithm": true, "scripts": {}, "sortAnswers": false, "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst"}], "metadata": {"licence": "All rights reserved", "description": ""}, "functions": {}, "rulesets": {}, "advice": "", "variablesTest": {"condition": "", "maxRuns": 100}, "variable_groups": [], "ungrouped_variables": ["int1", "int2", "years"], "type": "question"}, {"name": "2016-1b", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Swa Lup", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2902/"}], "metadata": {"licence": "None specified", "description": ""}, "ungrouped_variables": ["interest", "interest4"], "variablesTest": {"maxRuns": 100, "condition": ""}, "parts": [{"variableReplacementStrategy": "originalfirst", "sortAnswers": false, "prompt": "<p>The customer invests&nbsp;&pound;1,000 at time&nbsp;<em>t</em>=0. What nominal rate of interest, compounded quarterly, is earned over the first four year period?</p>\n<p>[[0]]%</p>", "type": "gapfill", "scripts": {}, "marks": 0, "extendBaseMarkingAlgorithm": true, "gaps": [{"marks": 1, "type": "numberentry", "scripts": {}, "showCorrectAnswer": true, "allowFractions": false, "maxValue": "{interest4}+0.02", "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "correctAnswerFraction": false, "minValue": "{interest4}-0.02", "showFeedbackIcon": true, "customMarkingAlgorithm": "", "mustBeReducedPC": 0, "mustBeReduced": false, "correctAnswerStyle": "plain", "notationStyles": ["plain", "en", "si-en"], "unitTests": [], "variableReplacements": []}], "showFeedbackIcon": true, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "unitTests": [], "variableReplacements": []}], "variable_groups": [], "functions": {}, "tags": [], "statement": "<p>A customer is offered an investment where interest is calculated according to the following force of interest</p>\n<p>\\[<br/> \\delta(t) =<br/> \\begin{cases}<br/> 0.02t &amp; 0\\leq t \\leq 3 \\\\<br/> 0.045 &amp; 3 \\leq t \\\\<br/> \\end{cases}<br/>\\]</p>", "rulesets": {}, "advice": "", "variables": {"interest4": {"name": "interest4", "group": "Ungrouped variables", "definition": "{interest}*(100)", "templateType": "anything", "description": ""}, "interest": {"name": "interest", "group": "Ungrouped variables", "definition": "((e^(0.135))^(1/16)-1)*4", "templateType": "anything", "description": ""}}, "preamble": {"css": "", "js": ""}, "type": "question"}, {"name": "2016-2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Swa Lup", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2902/"}], "parts": [{"scripts": {}, "gaps": [{"scripts": {}, "type": "numberentry", "extendBaseMarkingAlgorithm": true, "marks": 1, "variableReplacementStrategy": "originalfirst", "unitTests": [], "mustBeReducedPC": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "allowFractions": false, "correctAnswerStyle": "plain", "correctAnswerFraction": false, "customMarkingAlgorithm": "", "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "maxValue": "{n}+2.2", "mustBeReduced": false, "minValue": "{n}+1.8"}], "type": "gapfill", "extendBaseMarkingAlgorithm": true, "marks": 0, "variableReplacementStrategy": "originalfirst", "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "sortAnswers": false, "customMarkingAlgorithm": "", "variableReplacements": [], "prompt": "<p>(a) Given that the venture will be financed by bank loans on the basis of an effective annual interest rate of {int}% per annum and that the loans may be repaid continuously, find the discounted payback period for the project.&nbsp;</p>\n<p>Discounted payback period: [[0]] years</p>"}, {"scripts": {}, "gaps": [{"scripts": {}, "type": "numberentry", "extendBaseMarkingAlgorithm": true, "marks": 1, "variableReplacementStrategy": "originalfirst", "unitTests": [], "mustBeReducedPC": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "allowFractions": false, "correctAnswerStyle": "plain", "correctAnswerFraction": false, "customMarkingAlgorithm": "", "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "maxValue": "{acca}+1", "mustBeReduced": false, "minValue": "{acca}-1"}], "type": "gapfill", "extendBaseMarkingAlgorithm": true, "marks": 0, "variableReplacementStrategy": "originalfirst", "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "sortAnswers": false, "customMarkingAlgorithm": "", "variableReplacements": [], "prompt": "<p>(b) Given, further, that after the loans have been repaid the investor will deposit all the available income in an account which will earn interest at {int1}% per annum effective, find the accumulated amount of the account in 22 year's time.</p>\n<p>Accumulated amount:&nbsp;&pound;[[0]]</p>"}, {"scripts": {}, "gaps": [{"scripts": {}, "type": "numberentry", "extendBaseMarkingAlgorithm": true, "marks": 1, "variableReplacementStrategy": "originalfirst", "unitTests": [], "mustBeReducedPC": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "allowFractions": false, "correctAnswerStyle": "plain", "correctAnswerFraction": false, "customMarkingAlgorithm": "", "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "maxValue": "{period}+0.2", "mustBeReduced": false, "minValue": "{period}-0.2"}, {"scripts": {}, "type": "numberentry", "extendBaseMarkingAlgorithm": true, "marks": 1, "variableReplacementStrategy": "originalfirst", "unitTests": [], "mustBeReducedPC": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "allowFractions": false, "correctAnswerStyle": "plain", "correctAnswerFraction": false, "customMarkingAlgorithm": "", "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "maxValue": "{acc}+5", "mustBeReduced": false, "minValue": "{acc}-5"}], "type": "gapfill", "extendBaseMarkingAlgorithm": true, "marks": 0, "variableReplacementStrategy": "originalfirst", "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "sortAnswers": false, "customMarkingAlgorithm": "", "variableReplacements": [], "prompt": "<p>(c) Suppose that the bank loans may be repaid partially, but only at the end of each complete year, and that the investor may still deposit money at any time for any term at an annual rate of interest of {int2}% per annum effective. Find the discounted payback period for the project and the accumulated amount in the investor's account in 22 years' time. [Accept payment at the beginning of the year and pay at the end of the year]</p>\n<p>Discounted payback period: [[0]]years</p>\n<p>Accumulated amount:&nbsp;&pound;[[1]]</p>"}], "variables": {"teta": {"definition": "ln(1+{int2}/100)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "teta"}, "period": {"definition": "(log (1-{abc}{teta})/(log ({v1})))+2", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "period"}, "int": {"definition": "random(6..8#1)", "group": "Ungrouped variables", "templateType": "randrange", "description": "", "name": "int"}, "sn1": {"definition": "10000*(({int2}/100)/{teta})", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "sn1"}, "value1": {"definition": "random(4000..6000#1000)", "group": "Ungrouped variables", "templateType": "randrange", "description": "", "name": "value1"}, "value": {"definition": "random(90000..80000#5000)", "group": "Ungrouped variables", "templateType": "randrange", "description": "", "name": "value"}, "acc": {"definition": "10000*((1+{int2}/100)^(22-{period})-1)/{teta}", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "acc"}, "acca": {"definition": "10000{sn}", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "acca"}, "v1": {"definition": "1/(1+{int2}/100)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "v1"}, "n": {"definition": "(log (1-(ln(1+{int}/100)){an}))/(log({v}))", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "n"}, "v": {"definition": "(1/(1+{int}/100))", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "v"}, "sn": {"definition": "((1+{int1}/100)^(20-n)-1)/(ln(1+{int1}/100))", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "sn"}, "abc": {"definition": "(80000+5000{v1})/({sn1}*({v1}^2))", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "abc"}, "int2": {"definition": "random(5..7#1)", "group": "Ungrouped variables", "templateType": "randrange", "description": "", "name": "int2"}, "An": {"definition": "(80000+5000{v})/(10000*{v}^2)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "An"}, "int1": {"definition": "random(5..6#1)", "group": "Ungrouped variables", "templateType": "randrange", "description": "", "name": "int1"}}, "variable_groups": [], "metadata": {"description": "", "licence": "None specified"}, "advice": "", "rulesets": {}, "tags": [], "ungrouped_variables": ["value", "value1", "v", "int", "An", "n", "acca", "sn", "int1", "period", "acc", "int2", "sn1", "teta", "v1", "abc"], "functions": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "statement": "<p>An investor has decided to purchase a leasehold property for&nbsp;&pound;80,000 with a further payment of&nbsp;&pound;5,000 for repairs in one year's time. The income associated with letting the property will be&nbsp;&pound;10,000 per annum, payable continuously for 20 years commencing in two year's time. (2 years after repairs.)</p>", "preamble": {"js": "", "css": ""}, "type": "question"}, {"name": "2016-3a", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Swa Lup", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2902/"}], "preamble": {"js": "", "css": ""}, "statement": "", "ungrouped_variables": ["value", "int", "pvalue", "int1", "im", "pm"], "variables": {"im": {"description": "", "group": "Ungrouped variables", "definition": "(1+{int}/100)*(1+{int1}/100)-1", "name": "im", "templateType": "anything"}, "int1": {"description": "", "group": "Ungrouped variables", "definition": "random(2..4#1)", "name": "int1", "templateType": "randrange"}, "int": {"description": "", "group": "Ungrouped variables", "definition": "random(5..7#0.5)", "name": "int", "templateType": "randrange"}, "pvalue": {"description": "", "group": "Ungrouped variables", "definition": "{value}*(1/{pm})", "name": "pvalue", "templateType": "anything"}, "value": {"description": "", "group": "Ungrouped variables", "definition": "random(40000..70000#10000)", "name": "value", "templateType": "randrange"}, "pm": {"description": "", "group": "Ungrouped variables", "definition": "(1+{im})^3-1", "name": "pm", "templateType": "anything"}}, "variable_groups": [], "metadata": {"description": "", "licence": "None specified"}, "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "", "rulesets": {}, "parts": [{"variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "unitTests": [], "showCorrectAnswer": true, "variableReplacements": [], "marks": 0, "gaps": [{"type": "numberentry", "scripts": {}, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "minValue": "{pvalue}-30", "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "unitTests": [], "showCorrectAnswer": true, "variableReplacements": [], "maxValue": "{pvalue}30", "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "correctAnswerFraction": false, "marks": 1, "correctAnswerStyle": "plain", "showFeedbackIcon": true, "mustBeReduced": false}], "prompt": "<p>A perpetuity will make payments of&nbsp;&pound;{value} every third year, with the first payment occuring three years from now. Given an effective annual real rate of interest of {int}% per annum and an expected inflation rate of {int1}% per annum effective, find the present value of this perpetuity.</p>\n<p>Present value:&nbsp;&pound;[[0]]</p>", "sortAnswers": false, "scripts": {}, "type": "gapfill"}], "tags": [], "functions": {}, "type": "question"}, {"name": "2016-3b", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Swa Lup", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2902/"}], "preamble": {"js": "", "css": ""}, "statement": "<p>A loan is repayable by increasing annual instalments made in arrears for {year} years. The repayment at the end of the first year is&nbsp;&pound;{value} and subsequent payments increase by&nbsp;&pound;{value1} each year. The repayments were calculated using a rate of interest of {int}% per annum effective.</p>", "ungrouped_variables": ["value", "value1", "year", "int", "loan", "an", "v", "Ann", "d"], "variables": {"value1": {"definition": "random(150..250#50)", "group": "Ungrouped variables", "description": "", "templateType": "randrange", "name": "value1"}, "v": {"definition": "1/(1+{int}/100)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "v"}, "an": {"definition": "{value}*((1-{v}^{year})/({int}/100))", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "an"}, "year": {"definition": "random(10..20#5)", "group": "Ungrouped variables", "description": "", "templateType": "randrange", "name": "year"}, "d": {"definition": "({int}/100)/(1+{int}/100)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "d"}, "value": {"definition": "random(2000..4000#500)", "group": "Ungrouped variables", "description": "", "templateType": "randrange", "name": "value"}, "loan": {"definition": "{an}+{ann}", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "loan"}, "int": {"definition": "random(7..9#1)", "group": "Ungrouped variables", "description": "", "templateType": "randrange", "name": "int"}, "Ann": {"definition": "{v}*200*(((1-{v}^({year}-1))/{d})-({year}-1)*{v}^({year}-1))/({int}/100)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "Ann"}}, "variable_groups": [], "metadata": {"description": "", "licence": "None specified"}, "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "", "rulesets": {}, "parts": [{"variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "gaps": [{"variableReplacementStrategy": "originalfirst", "type": "numberentry", "customMarkingAlgorithm": "", "allowFractions": false, "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "{loan}-5", "variableReplacements": [], "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "correctAnswerFraction": false, "maxValue": "{loan}+5", "scripts": {}, "correctAnswerStyle": "plain", "showFeedbackIcon": true, "mustBeReduced": false, "marks": 1}], "unitTests": [], "showCorrectAnswer": true, "variableReplacements": [], "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "prompt": "<p>(a) Calculate the original amount of the loan.&nbsp;&pound;[[0]]</p>", "sortAnswers": false, "scripts": {}, "type": "gapfill", "marks": 0}], "tags": [], "functions": {}, "type": "question"}, {"name": "2016-4a", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Swa Lup", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2902/"}], "preamble": {"js": "", "css": ""}, "statement": "<p>List the main features of&nbsp;</p>", "ungrouped_variables": [], "variables": {}, "variable_groups": [], "metadata": {"description": "", "licence": "None specified"}, "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "", "rulesets": {}, "parts": [{"variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "gaps": [{"displayType": "radiogroup", "matrix": [["0", "1"], ["0", "1"], ["1", "0"], ["1", "0"], ["0", "1"], [0, 0]], "choices": ["Issued by goverment", "Secure", "Unsecure", "Currency issued other than the issuer's country currency and is a country other than the issuer's home country.", "linked to an index which reflect the effects of inflation", "Cheap"], "showCellAnswerState": true, "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "variableReplacements": [], "warningType": "none", "maxAnswers": 0, "answers": ["EuroBonds", "Index Linked Government bonds"], "scripts": {}, "marks": 0, "minAnswers": 0, "shuffleChoices": false, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "maxMarks": 0, "unitTests": [], "showFeedbackIcon": true, "shuffleAnswers": false, "layout": {"expression": "", "type": "all"}, "minMarks": 0, "type": "m_n_x"}], "unitTests": [], "showCorrectAnswer": true, "variableReplacements": [], "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "prompt": "<p>(i) Eurobonds</p>\n<p>(ii) Index linked government bonds</p>\n<p>[[0]]</p>\n<p></p>", "sortAnswers": false, "scripts": {}, "type": "gapfill", "marks": 0}], "tags": [], "functions": {}, "type": "question"}, {"name": "2016-4b", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Swa Lup", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2902/"}], "rulesets": {}, "variables": {"v1": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "(1/(1+{int2}/100))^2", "name": "v1"}, "i2": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "(sqrt(1+{int1}/100)-1)*2", "name": "i2"}, "below": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "1-({tax1}/100)*{v1}", "name": "below"}, "int": {"description": "", "group": "Ungrouped variables", "templateType": "randrange", "definition": "random(8..10#1)", "name": "int"}, "a2": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "(1-(1/(1+{int1}/100))^10)/{i2}", "name": "a2"}, "i22": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "(sqrt(1+{int2}/100)-1)*2", "name": "i22"}, "tax1": {"description": "", "group": "Ungrouped variables", "templateType": "randrange", "definition": "random(35..40#5)", "name": "tax1"}, "tax": {"description": "", "group": "Ungrouped variables", "templateType": "randrange", "definition": "random(20..30#5)", "name": "tax"}, "a22": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "(1-(1/(1+{int2}/100))^2)/{i22}", "name": "a22"}, "int2": {"description": "", "group": "Ungrouped variables", "templateType": "randrange", "definition": "random(6..7#1)", "name": "int2"}, "price": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "(1-({tax}/100))*100({int}/100){a2}+110(1/(1+{int1}/100))^10", "name": "price"}, "int1": {"description": "", "group": "Ungrouped variables", "templateType": "randrange", "definition": "random(7..9#1)", "name": "int1"}, "price1": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "((1-({tax1}/100))*100({int}/100){a22}+110{v1}-(({tax1}/100)*110)*{v1})/{below}", "name": "price1"}}, "variable_groups": [], "metadata": {"description": "", "licence": "None specified"}, "advice": "", "parts": [{"scripts": {}, "gaps": [{"scripts": {}, "type": "numberentry", "extendBaseMarkingAlgorithm": true, "marks": 1, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "mustBeReducedPC": 0, "unitTests": [], "showFeedbackIcon": true, "allowFractions": false, "correctAnswerStyle": "plain", "correctAnswerFraction": false, "customMarkingAlgorithm": "", "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "maxValue": "{price}+1", "mustBeReduced": false, "minValue": "{price}-1"}], "type": "gapfill", "extendBaseMarkingAlgorithm": true, "marks": 0, "variableReplacementStrategy": "originalfirst", "unitTests": [], "sortAnswers": false, "showFeedbackIcon": true, "showCorrectAnswer": true, "customMarkingAlgorithm": "", "variableReplacements": [], "prompt": "<p>(i) An investor, subject to income tax at {tax}% but not liable to capital gains tax, bought&nbsp;&pound;10,000 nominal of the stock at issue so as to obtain a net effective yielf of {int1}% per annum, after tax. What price did the investor pay per&nbsp;&pound;100 nominal on the date of issue?</p>\n<p>Price:&pound;[[0]]</p>"}, {"scripts": {}, "gaps": [{"scripts": {}, "choices": ["Yes", "No"], "customMarkingAlgorithm": "", "maxMarks": 0, "type": "1_n_2", "extendBaseMarkingAlgorithm": true, "distractors": ["", ""], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "marks": 0, "shuffleChoices": false, "unitTests": [], "showFeedbackIcon": true, "displayColumns": 0, "showCorrectAnswer": true, "minMarks": 0, "showCellAnswerState": true, "variableReplacements": [], "matrix": ["1", 0]}, {"scripts": {}, "type": "numberentry", "extendBaseMarkingAlgorithm": true, "marks": 1, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "mustBeReducedPC": 0, "unitTests": [], "showFeedbackIcon": true, "allowFractions": false, "correctAnswerStyle": "plain", "correctAnswerFraction": false, "customMarkingAlgorithm": "", "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "maxValue": "{price1}+1", "mustBeReduced": false, "minValue": "{price1}-1"}], "type": "gapfill", "extendBaseMarkingAlgorithm": true, "marks": 0, "variableReplacementStrategy": "originalfirst", "unitTests": [], "sortAnswers": false, "showFeedbackIcon": true, "showCorrectAnswer": true, "customMarkingAlgorithm": "", "variableReplacements": [], "prompt": "<p>(ii) On 1 January 2014, the first investor, having received the interest due on that date, sold the stock to a second investor who was subject to {tax1}% tax on both income and capital gains. The price paid by the second investor was calculated so as to earn him a net effective yield of {int2}% per annum, after tax. Is the CGT payable? What price did the second investor pay per&nbsp;&pound;100 nominal?</p>\n<p>CGT payable?[[0]]&nbsp;</p>\n<p>Price: &pound;[[1]]</p>\n<p></p>"}], "tags": [], "ungrouped_variables": ["tax", "int", "int1", "price", "i2", "a2", "tax1", "int2", "price1", "i22", "a22", "v1", "below"], "functions": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "statement": "<p>Ten millions pound nominal of loan stock was issued on 1 January 2006. The stock is due to be redeemed in one payment of 110% nominal on 1 January 2016. The stock pays interest at {int}% per annum, payable half-yearly in arrears on 1 June and 1 January.</p>", "preamble": {"js": "", "css": ""}, "type": "question"}, {"name": "2016-5a", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Swa Lup", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2902/"}], "variables": {}, "ungrouped_variables": [], "functions": {}, "advice": "", "statement": "", "variablesTest": {"maxRuns": 100, "condition": ""}, "metadata": {"licence": "None specified", "description": ""}, "variable_groups": [], "preamble": {"js": "", "css": ""}, "tags": [], "rulesets": {}, "parts": [{"showCorrectAnswer": true, "gaps": [{"showCorrectAnswer": true, "displayType": "checkbox", "minMarks": 0, "distractors": ["", "", ""], "customMarkingAlgorithm": "", "scripts": {}, "marks": 0, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "type": "m_n_2", "warningType": "none", "showCellAnswerState": true, "maxMarks": 0, "choices": ["PV<sub>a&nbsp;</sub>= PV<sub>L</sub>", "PV<sub>a&nbsp;</sub>&lt;&nbsp;PV<sub>L</sub>", "PV<sub>a&nbsp;</sub>&gt;&nbsp;PV<sub>L</sub>"], "displayColumns": 0, "unitTests": [], "minAnswers": 0, "shuffleChoices": false, "matrix": ["1", 0, 0], "showFeedbackIcon": true, "maxAnswers": 0}, {"showCorrectAnswer": true, "displayType": "radiogroup", "minMarks": 0, "distractors": ["", "", ""], "customMarkingAlgorithm": "", "choices": ["D<sub>a&nbsp;</sub>= D<sub>L</sub>", "D<sub>a&nbsp;</sub>&lt; D<sub>L</sub>", "D<sub>a&nbsp;</sub>&gt;&nbsp;D<sub>L</sub>"], "scripts": {}, "displayColumns": 0, "marks": 0, "unitTests": [], "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "shuffleChoices": false, "variableReplacementStrategy": "originalfirst", "maxMarks": 0, "type": "1_n_2", "showCellAnswerState": true, "showFeedbackIcon": true, "matrix": ["1", 0, 0]}, {"showCorrectAnswer": true, "displayType": "radiogroup", "minMarks": 0, "distractors": ["", "", ""], "customMarkingAlgorithm": "", "choices": ["K<sub>a&nbsp;</sub>= K<sub>L</sub>", "K<sub>a&nbsp;</sub>&lt;&nbsp;K<sub>L</sub>", "K<sub>a&nbsp;</sub>&gt;&nbsp;K<sub>L</sub>"], "scripts": {}, "displayColumns": 0, "marks": 0, "unitTests": [], "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "shuffleChoices": false, "variableReplacementStrategy": "originalfirst", "maxMarks": 0, "type": "1_n_2", "showCellAnswerState": true, "showFeedbackIcon": true, "matrix": [0, 0, "1"]}], "customMarkingAlgorithm": "", "scripts": {}, "sortAnswers": false, "variableReplacements": [], "unitTests": [], "marks": 0, "extendBaseMarkingAlgorithm": true, "prompt": "<p>State the Redington's conditions for immunisation of a portfolio of assets and liabilities against small changes in interest rates.</p>\n<p>[[0]]</p>\n<p>[[1]]</p>\n<p>[[2]]</p>", "variableReplacementStrategy": "originalfirst", "type": "gapfill", "showFeedbackIcon": true}], "type": "question"}, {"name": "2016-5b", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Swa Lup", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2902/"}], "variable_groups": [], "parts": [{"gaps": [{"correctAnswerFraction": false, "unitTests": [], "minValue": "{pv}-1", "showCorrectAnswer": true, "showFeedbackIcon": true, "allowFractions": false, "marks": 1, "variableReplacements": [], "correctAnswerStyle": "plain", "type": "numberentry", "mustBeReduced": false, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "maxValue": "{pv}+1", "mustBeReducedPC": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst"}, {"correctAnswerFraction": false, "unitTests": [], "minValue": "{D}-0.2", "showCorrectAnswer": true, "showFeedbackIcon": true, "allowFractions": false, "marks": 1, "variableReplacements": [], "correctAnswerStyle": "plain", "type": "numberentry", "mustBeReduced": false, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "maxValue": "{D}+0.2", "mustBeReducedPC": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst"}], "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "unitTests": [], "type": "gapfill", "variableReplacements": [], "prompt": "<p>(i) Calculate the present value and volatility of the liability cash flows.</p>\n<p>Present value:&nbsp;&pound;[[0]]</p>\n<p>volatility: [[1]]years</p>", "scripts": {}, "variableReplacementStrategy": "originalfirst", "sortAnswers": false, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true}, {"gaps": [{"correctAnswerFraction": false, "unitTests": [], "minValue": "{x}-20", "showCorrectAnswer": true, "showFeedbackIcon": true, "allowFractions": false, "marks": 1, "variableReplacements": [], "correctAnswerStyle": "plain", "type": "numberentry", "mustBeReduced": false, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "maxValue": "{x}+20", "mustBeReducedPC": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst"}, {"correctAnswerFraction": false, "unitTests": [], "minValue": "{n}-0.2", "showCorrectAnswer": true, "showFeedbackIcon": true, "allowFractions": false, "marks": 1, "variableReplacements": [], "correctAnswerStyle": "plain", "type": "numberentry", "mustBeReduced": false, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "maxValue": "{n}+0.2", "mustBeReducedPC": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst"}], "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "unitTests": [], "type": "gapfill", "variableReplacements": [], "prompt": "<p>(ii) Determine the values of X and&nbsp;<em>n</em> such that the first two conditions of Redington's immunisation theory are satisfied.</p>\n<p>X:&nbsp;&pound;[[0]]&nbsp; , n: [[1]] years</p>", "scripts": {}, "variableReplacementStrategy": "originalfirst", "sortAnswers": false, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true}], "preamble": {"css": "", "js": ""}, "advice": "", "variables": {"D": {"templateType": "anything", "group": "Ungrouped variables", "name": "D", "description": "", "definition": "((6*7{v}^6+9*{v}^9+2*11{v}^11)*100000)/{pv}"}, "a55": {"templateType": "anything", "group": "Ungrouped variables", "name": "a55", "description": "", "definition": "((1+{int}/100)*{a5}-5{v}^5)/({int}/100)"}, "n": {"templateType": "anything", "group": "Ungrouped variables", "name": "n", "description": "", "definition": "(((6*7{v}^6+9*{v}^9+2*11{v}^11)*100000)-15000{a55}-1500000{v}^5)/{xvn}"}, "v": {"templateType": "anything", "group": "Ungrouped variables", "name": "v", "description": "", "definition": "(1/(1+{int}/100))"}, "int": {"templateType": "randrange", "group": "Ungrouped variables", "name": "int", "description": "", "definition": "random(6..8#1)"}, "a5": {"templateType": "anything", "group": "Ungrouped variables", "name": "a5", "description": "", "definition": "(1-(1/(1+{int}/100))^5)/({int}/100)"}, "pv": {"templateType": "anything", "group": "Ungrouped variables", "name": "pv", "description": "", "definition": "(7{v}^6+{v}^9+2{v}^11)*100000"}, "xvn": {"templateType": "anything", "group": "Ungrouped variables", "name": "xvn", "description": "", "definition": "{pv}-(15000{a5}+300000(1/(1+{int}/100))^5)"}, "x": {"templateType": "anything", "group": "Ungrouped variables", "name": "x", "description": "", "definition": "{xvn}/{v}^n"}}, "statement": "<p>A pension fund has the following liabilities:</p>\n<p>&nbsp; &nbsp;&pound;700,000 payable at the end of 6 year,</p>\n<p>&nbsp; &nbsp;&pound;100,000 payable at the end of 9 year and,</p>\n<p>&nbsp; &nbsp;&pound;200,000 payable at the end of 11 year.</p>\n<p>The fund holds the following two assets to meet the liabilities:</p>\n<p>&nbsp; Investment A: which provides income of&nbsp;&pound;15,000 payable at the end of each year for the next five years and additionally a lump sum of&nbsp;&pound;300,000 payable at the end of 5<sup>th</sup> year.</p>\n<p>&nbsp; Investment B: which is a zero coupon bond which pays a lump sum of&nbsp;&pound;X at the end of&nbsp;<em>n</em> years (where&nbsp;<em>n</em> is not necessarily an integer).</p>\n<p>The interest rate is {int}% per annum effective.</p>", "ungrouped_variables": ["pv", "D", "v", "int", "x", "n", "a5", "xvn", "a55"], "rulesets": {}, "tags": [], "functions": {}, "variablesTest": {"maxRuns": 100, "condition": ""}, "metadata": {"licence": "None specified", "description": ""}, "type": "question"}, {"name": "2016-6", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Swa Lup", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2902/"}], "variables": {"price": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "({k}-{payment})*(e^(-0.5*{int}/100))", "name": "price"}, "forward": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "(10-e^(-(3/12)*{int}/100))/(e^(-0.5*{int}/100))", "name": "forward"}, "payment": {"templateType": "randrange", "description": "", "group": "Ungrouped variables", "definition": "random(9..10#0.5)", "name": "payment"}, "k": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "10/e^(-0.5*{int}/100)", "name": "k"}, "arb": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "{forward}-8", "name": "arb"}, "int": {"templateType": "randrange", "description": "", "group": "Ungrouped variables", "definition": "random(3..6#1)", "name": "int"}}, "ungrouped_variables": ["k", "int", "price", "payment", "forward", "arb"], "advice": "", "functions": {}, "statement": "<p>We consider a stock whose price today is&nbsp;&pound;10. The risk free force of interest is {int}% effective per annum. Assume that the stock will not pay dividends during the next 6 months.</p>", "variablesTest": {"maxRuns": 100, "condition": ""}, "metadata": {"licence": "None specified", "description": ""}, "variable_groups": [], "preamble": {"js": "", "css": ""}, "tags": [], "rulesets": {}, "parts": [{"showCorrectAnswer": true, "gaps": [{"showCorrectAnswer": true, "maxValue": "{k}+0.1", "notationStyles": ["plain", "en", "si-en"], "customMarkingAlgorithm": "", "mustBeReducedPC": 0, "scripts": {}, "mustBeReduced": false, "marks": 1, "unitTests": [], "minValue": "{k}-0.1", "variableReplacements": [], "allowFractions": false, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "type": "numberentry", "showFeedbackIcon": true, "correctAnswerFraction": false}], "customMarkingAlgorithm": "", "scripts": {}, "sortAnswers": false, "variableReplacements": [], "unitTests": [], "marks": 0, "extendBaseMarkingAlgorithm": true, "prompt": "<p>(a) Calculate the forward price of this stock.&nbsp;&pound;[[0]]</p>", "variableReplacementStrategy": "originalfirst", "type": "gapfill", "showFeedbackIcon": true}, {"showCorrectAnswer": true, "gaps": [{"showCorrectAnswer": true, "maxValue": "{price}+0.02", "notationStyles": ["plain", "en", "si-en"], "customMarkingAlgorithm": "", "mustBeReducedPC": 0, "scripts": {}, "mustBeReduced": false, "marks": 1, "unitTests": [], "minValue": "{price}-0.02", "variableReplacements": [], "allowFractions": false, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "type": "numberentry", "showFeedbackIcon": true, "correctAnswerFraction": false}], "customMarkingAlgorithm": "", "scripts": {}, "sortAnswers": false, "variableReplacements": [], "unitTests": [], "marks": 0, "extendBaseMarkingAlgorithm": true, "prompt": "<p>(b) An investor is offered the opportunity to enter into a long position in an existing forward contract with delivery price&nbsp;&pound;{payment} that expires in 6 months. What is the highest price that the investor is ready to pay for this forward contract?</p>\n<p>Highest price: &pound;[[0]]</p>", "variableReplacementStrategy": "originalfirst", "type": "gapfill", "showFeedbackIcon": true}, {"showCorrectAnswer": true, "gaps": [{"showCorrectAnswer": true, "maxValue": "{forward}+0.1", "notationStyles": ["plain", "en", "si-en"], "customMarkingAlgorithm": "", "mustBeReducedPC": 0, "scripts": {}, "mustBeReduced": false, "marks": 1, "unitTests": [], "minValue": "{forward}-0.1", "variableReplacements": [], "allowFractions": false, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "type": "numberentry", "showFeedbackIcon": true, "correctAnswerFraction": false}, {"showCorrectAnswer": true, "maxValue": "{arb}+0.1", "notationStyles": ["plain", "en", "si-en"], "customMarkingAlgorithm": "", "mustBeReducedPC": 0, "scripts": {}, "mustBeReduced": false, "marks": 1, "unitTests": [], "minValue": "{arb}-0.1", "variableReplacements": [], "allowFractions": false, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "type": "numberentry", "showFeedbackIcon": true, "correctAnswerFraction": false}], "customMarkingAlgorithm": "", "scripts": {}, "sortAnswers": false, "variableReplacements": [], "unitTests": [], "marks": 0, "extendBaseMarkingAlgorithm": true, "prompt": "<p>(c) Now assume that the stock will pay a dividend of&nbsp;&pound;1 in 3 months time.</p>\n<p>&nbsp; &nbsp;(i) Calculate the forward price of the stock in this situation.&nbsp;&pound;[[0]]</p>\n<p>&nbsp; &nbsp;(ii)Explain how you can make an arbitrage profit if you are offered to buy the stock for&nbsp;&pound;8 in 6 months time without any additional payment today or later. To construct an arbitrafe portfolio you should only use the stock, the risk-free force of interest and the forward contract. How much arbitrage profit you can make with one forward contract?</p>\n<p>Arbitrage profit:&nbsp;&pound;[[1]]</p>", "variableReplacementStrategy": "originalfirst", "type": "gapfill", "showFeedbackIcon": true}], "type": "question"}, {"name": "2016-8", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Swa Lup", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2902/"}], "rulesets": {}, "tags": [], "variable_groups": [], "metadata": {"description": "", "licence": "None specified"}, "advice": "", "parts": [{"showFeedbackIcon": true, "variableReplacements": [], "type": "gapfill", "extendBaseMarkingAlgorithm": true, "marks": 0, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "sortAnswers": false, "scripts": {}, "unitTests": [], "customMarkingAlgorithm": "", "gaps": [{"showFeedbackIcon": true, "type": "numberentry", "extendBaseMarkingAlgorithm": true, "marks": 1, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "mustBeReducedPC": 0, "scripts": {}, "unitTests": [], "allowFractions": false, "correctAnswerStyle": "plain", "correctAnswerFraction": false, "customMarkingAlgorithm": "", "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "maxValue": "{invested}+20", "mustBeReduced": false, "minValue": "{invested}-20"}], "prompt": "<p>(a) Calculate the amount invested.&nbsp;&pound;[[0]]</p>"}, {"showFeedbackIcon": true, "variableReplacements": [], "type": "gapfill", "extendBaseMarkingAlgorithm": true, "marks": 0, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "sortAnswers": false, "scripts": {}, "unitTests": [], "customMarkingAlgorithm": "", "gaps": [{"showFeedbackIcon": true, "type": "numberentry", "extendBaseMarkingAlgorithm": true, "marks": 1, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "mustBeReducedPC": 0, "scripts": {}, "unitTests": [], "allowFractions": false, "correctAnswerStyle": "plain", "correctAnswerFraction": false, "customMarkingAlgorithm": "", "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "maxValue": "{profit}+1", "mustBeReduced": false, "minValue": "{profit}-1"}], "prompt": "<p>(b) Calculate the expected pro\ufb01t of the fund due to this investment at the end of \ufb01ve years.&nbsp;</p>\n<p>Expected profit:&nbsp;&pound;[[0]]</p>"}, {"showFeedbackIcon": true, "variableReplacements": [], "type": "gapfill", "extendBaseMarkingAlgorithm": true, "marks": 0, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "sortAnswers": false, "scripts": {}, "unitTests": [], "customMarkingAlgorithm": "", "gaps": [{"showFeedbackIcon": true, "type": "numberentry", "extendBaseMarkingAlgorithm": true, "marks": 1, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "mustBeReducedPC": 0, "scripts": {}, "unitTests": [], "allowFractions": false, "correctAnswerStyle": "plain", "correctAnswerFraction": false, "customMarkingAlgorithm": "", "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "maxValue": "{k}+0.00001", "mustBeReduced": false, "minValue": "{k}-0.00001"}], "prompt": "<p>(c) The monthly return i on a fund has a mean of 1.70% and standard deviation of 2%. Assume that (1 + <em>i</em>) is log normally distributed. Calculate the value of k such that the probability of i being greater than k is 80%.&nbsp;&nbsp;</p>\n<p>k=[[0]] (not in %)</p>"}], "variables": {"profit": {"definition": "{invested}*(0.2*(1+{int}/100)^5+({percent}/100)*(1+{int1}/100)^5+({percent1}/100)*(1+{int2}/100)^5)-20000", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "profit"}, "percent": {"definition": "random(40..50#5)", "group": "Ungrouped variables", "templateType": "randrange", "description": "", "name": "percent"}, "int2": {"definition": "{int}+4", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "int2"}, "ei": {"definition": "({int}*0.2+{int1}*{percent}/100+{int2}*{percent1}/100)/100", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "ei"}, "int": {"definition": "random(4..6#1)", "group": "Ungrouped variables", "templateType": "randrange", "description": "", "name": "int"}, "k": {"definition": "0.000106885", "group": "Ungrouped variables", "templateType": "number", "description": "", "name": "k"}, "percent1": {"definition": "80-{percent}", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "percent1"}, "int1": {"definition": "{int}+2", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "int1"}, "invested": {"definition": "20000/(1+{ei})^5", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "invested"}}, "ungrouped_variables": ["int", "int1", "int2", "percent", "percent1", "invested", "ei", "profit", "k"], "functions": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "statement": "<p>A fund has a liability to pay &pound;20,000 at the end of \ufb01ve years. To meet its liability, the fund manager invests in \ufb01ve-year zero coupon bonds which provides any one of the annual effective return of {int}% or {int1}% or {int2}% with probability 0.2,{percent} and {percent1} respectively over the next \ufb01ve years. The fund manager invests the present value of the liability at the expected rate of interest it would earn on the zero-coupon bond.</p>", "preamble": {"js": "", "css": ""}, "type": "question"}, {"name": "2015-8", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Swa Lup", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2902/"}], "rulesets": {}, "variables": {}, "variable_groups": [], "metadata": {"description": "", "licence": "None specified"}, "advice": "", "parts": [{"scripts": {}, "gaps": [{"scripts": {}, "type": "numberentry", "extendBaseMarkingAlgorithm": true, "marks": 1, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "mustBeReducedPC": 0, "unitTests": [], "showFeedbackIcon": true, "allowFractions": false, "correctAnswerStyle": "plain", "correctAnswerFraction": false, "customMarkingAlgorithm": "", "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "maxValue": "3258.185", "mustBeReduced": false, "minValue": "3257.395"}], "type": "gapfill", "extendBaseMarkingAlgorithm": true, "marks": 0, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "unitTests": [], "showFeedbackIcon": true, "sortAnswers": false, "customMarkingAlgorithm": "", "variableReplacements": [], "prompt": "<p>Calculate the expected value of an investment of &pound;2,000 after 10 years.</p>\n<p>&pound;[[0]]</p>"}, {"scripts": {}, "gaps": [{"scripts": {}, "type": "numberentry", "extendBaseMarkingAlgorithm": true, "marks": 1, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "mustBeReducedPC": 0, "unitTests": [], "showFeedbackIcon": true, "allowFractions": false, "correctAnswerStyle": "plain", "correctAnswerFraction": false, "customMarkingAlgorithm": "", "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "maxValue": "43", "mustBeReduced": false, "minValue": "41"}], "type": "gapfill", "extendBaseMarkingAlgorithm": true, "marks": 0, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "unitTests": [], "showFeedbackIcon": true, "sortAnswers": false, "customMarkingAlgorithm": "", "variableReplacements": [], "prompt": "<p>&nbsp;Calculate the probability that the accumulated of the investment after 10 years will be less than 90% of the expected value from (a).&nbsp;</p>\n<p>[[0]]%</p>"}], "tags": [], "ungrouped_variables": [], "functions": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "statement": "<p>The rate of interest earned on a particular investment in different years are independently and identically distributed. Each year the distribution of (1 + <em>it</em>) is log-normal, where <em>it </em>is the return in year<em> t</em>. The annual rates have mean of 5% and standard deviation of 10%.</p>", "preamble": {"js": "", "css": ""}, "type": "question"}]}], "showstudentname": true, "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "feedback": {"allowrevealanswer": false, "feedbackmessages": [], "showactualmark": true, "showtotalmark": true, "intro": "", "advicethreshold": 0, "showanswerstate": true}, "type": "exam", "contributors": [{"name": "Swa Lup", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2902/"}], "extensions": [], "custom_part_types": [], "resources": []}