// Numbas version: exam_results_page_options
{"showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questions": [{"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": "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": "2016-8", "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"}]}], "type": "exam", "percentPass": "40", "duration": 10800, "navigation": {"reverse": true, "showfrontpage": true, "browse": true, "onleave": {"action": "none", "message": ""}, "allowregen": false, "showresultspage": "oncompletion", "preventleave": true}, "name": "Junlei's copy of Exam test 1(2016)", "showQuestionGroupNames": false, "feedback": {"advicethreshold": 0, "showtotalmark": true, "intro": "", "feedbackmessages": [], "showactualmark": true, "showanswerstate": true, "allowrevealanswer": false}, "metadata": {"description": "<p>Exam test 1/ 2016 past paper</p>", "licence": "Creative Commons Attribution 4.0 International"}, "timing": {"timedwarning": {"action": "none", "message": ""}, "allowPause": false, "timeout": {"action": "none", "message": ""}}, "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": []}