// Numbas version: exam_results_page_options
{"navigation": {"allowregen": false, "showresultspage": "oncompletion", "browse": true, "onleave": {"action": "none", "message": ""}, "showfrontpage": true, "reverse": true, "preventleave": true}, "feedback": {"showtotalmark": true, "showanswerstate": true, "allowrevealanswer": false, "showactualmark": true, "intro": "", "feedbackmessages": [], "advicethreshold": 0}, "showstudentname": true, "showQuestionGroupNames": false, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": ""}, "name": "Junlei's copy of Exam Test 2 (2015)", "duration": 10800, "timing": {"timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}, "allowPause": false}, "question_groups": [{"pickingStrategy": "all-ordered", "name": "Group", "pickQuestions": 1, "questions": [{"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": "2015-3b", "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": "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"}]}], "percentPass": "40", "type": "exam", "contributors": [{"name": "Swa Lup", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2902/"}, {"name": "Junlei Hu", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3534/"}], "extensions": [], "custom_part_types": [], "resources": []}