// Numbas version: exam_results_page_options
{"name": "MATH1510 Financial Mathematics 1 Practical 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {"growthy": {"definition": "var cells = [value];\nvar inty = 1 + ((int1/100) / 1);\n\nfor (i=0; i<m+1; i++) {\nvar growthy = (value)*math.pow(inty,math.floor(i / (12/ 1)));\ncells.push(growthy);\n}\n\nreturn cells;", "type": "list", "parameters": [["value", "number"], ["int1", "number"], ["m", "number"]], "language": "javascript"}, "growthm": {"definition": "var cells = [value];\nvar intm = 1 + ((int12/100) / 12);\n\nfor (i=0; i<m+1; i++) {\nvar growthm = (value)*math.pow(intm,math.floor(i / (12/ 12)));\ncells.push(growthm);\n}\n\nreturn cells;", "type": "list", "parameters": [["value", "number"], ["int12", "number"], ["m", "number"]], "language": "javascript"}, "growthq": {"definition": "var cells = [value];\nvar intq = 1 + ((int4/100) / 4);\n\nfor (i=0; i<m+1; i++) {\nvar growthq = (value)*math.pow(intq,math.floor(i / (12/ 4)));\ncells.push(growthq);\n}\n\nreturn cells;", "type": "list", "parameters": [["value", "number"], ["int4", "number"], ["m", "number"]], "language": "javascript"}}, "ungrouped_variables": ["int12", "int4", "int1", "value", "m", "value1", "value2", "sum", "interest1", "monthsa", "ceila", "interest2", "monthsb", "ceilb", "monthsc", "ceilc", "growthm", "growthq", "growthy", "targetm", "targetq", "targety", "Month1", "ceiltargetm", "ceiltargetq", "ceiltargety"], "name": "MATH1510 Financial Mathematics 1 Practical 1", "tags": [], "advice": "<p style=\"padding-left: 30px;\">1. Firstly, remember that the interest rate payable p-thly must be converted into the interest rate per period using $i_{[p]}={i^{(p)} \\over p}$</p>\n<p>As interest is gained on the balance, you must multiply the initial value, $x$&nbsp;of the previous month by the interest rate to the power of the month in which the interest is received:</p>\n<p style=\"text-align: center;\">$x(1+i_{[p]})^{floor({month \\over {12 \\over p}},1)}$</p>\n<p style=\"text-align: left;\">where:</p>\n<ul>\n<li>The $floor$ function rounds the number DOWN&nbsp;to the nearest integer.</li>\n</ul>\n<p>In order to find out the potential growth at a particular month, substitute in the relevant number.</p>\n<p style=\"padding-left: 30px;\">2. In order to see how many months one must keep an initial amount in an account so that it accumulates to a certain sum, you must find out what $n$ is in the formula:</p>\n<p style=\"text-align: center;\">$n={12 \\over p}{ln({accum \\over initial}) \\over ln({1+ i_{[p]}})}$</p>\n<p style=\"text-align: left;\">where:</p>\n<ul>\n<li>$ln$ is the natural logarithm.</li>\n</ul>\n<p>In order to see how many months you must keep it in the account,</p>\n<p style=\"text-align: center;\">$months={12 \\over p}ceiling({pn \\over 12},1)$</p>\n<p style=\"text-align: left;\">where:</p>\n<ul>\n<li>The $ceiling$ function rounds the number UP&nbsp;to the nearest integer.</li>\n</ul>\n<p>Substituting in the numbers in the question will give you the number of months.</p>", "rulesets": {}, "parts": [{"prompt": "<p>What is the sum (to two decimal places) of the potential growth corresponding to months {m-38}, {m-29}, {m-22}, {m-16}, {m-9}, {m-3} and {m} for each of&nbsp;the accounts?</p>\n<p><span>Monthly: [[0]]</span></p>\n<p><span>Quarterly: [[1]]</span></p>\n<p><span>Yearly: [[2]]</span></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "<p>You have not given your answer to two decimal places.</p>", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "{growthm[m-37]}+{growthm[m-28]}+{growthm[m-21]}+{growthm[m-15]}+{growthm[m-8]}+{growthm[m-2]}+{growthm[m+1]}", "minValue": "{growthm[m-37]}+{growthm[m-28]}+{growthm[m-21]}+{growthm[m-15]}+{growthm[m-8]}+{growthm[m-2]}+{growthm[m+1]}", "variableReplacementStrategy": "originalfirst", "strictPrecision": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "scripts": {}, "marks": "5", "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "<p>You have not given your answer to two decimal places.</p>", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "{growthq[m-37]}+{growthq[m-28]}+{growthq[m-21]}+{growthq[m-15]}+{growthq[m-8]}+{growthq[m-2]}+{growthq[m+1]}", "minValue": "{growthq[m-37]}+{growthq[m-28]}+{growthq[m-21]}+{growthq[m-15]}+{growthq[m-8]}+{growthq[m-2]}+{growthq[m+1]}", "variableReplacementStrategy": "originalfirst", "strictPrecision": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "scripts": {}, "marks": "5", "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "<p>You have not given your answer to two decimal places.</p>", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "{growthy[m-37]}+{growthy[m-28]}+{growthy[m-21]}+{growthy[m-15]}+{growthy[m-8]}+{growthy[m-2]}+{growthy[m+1]}", "minValue": "{growthy[m-37]}+{growthy[m-28]}+{growthy[m-21]}+{growthy[m-15]}+{growthy[m-8]}+{growthy[m-2]}+{growthy[m+1]}", "variableReplacementStrategy": "originalfirst", "strictPrecision": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "scripts": {}, "marks": "5", "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p><span>For each account, how long (in months) will it take for the balance to reach &pound;{value1}?</span></p>\n<p><span>Monthly: [[0]]</span></p>\n<p><span>Quarterly: [[1]]</span></p>\n<p>Yearly: [[2]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ceiltargetm}", "minValue": "{ceiltargetm}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": "2", "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ceiltargetq}", "minValue": "{ceiltargetq}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": "2", "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ceiltargety}", "minValue": "{ceiltargety}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": "2", "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>Construct a spreadsheet that will analytically compute the number of months a certain amount should be held in these accounts in order for this value to accumulate to a certain sum.</p>\n<p>Calculate the number of months you will need to hold &pound;{value2} in each of the accounts so that it reaches &pound;{sum}.</p>\n<p>Monthly:<i> [[0]]</i></p>\n<p>Quarterly:<i> [[1]]</i></p>\n<p>Yearly:<i> [[2]]</i></p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "ceila", "minValue": "ceila", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": "5", "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "ceilb", "minValue": "ceilb", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": "5", "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "ceilc", "minValue": "ceilc", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": "5", "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>A bank offers you three savings account:</p>\n<p style=\"padding-left: 30px;\">a) with nominal interest payable monthly into the account at a rate of {int12}%</p>\n<p style=\"padding-left: 30px;\">b) with nominal interest payable quaterly&nbsp;into the account at a rate of {int4}%</p>\n<p style=\"padding-left: 30px;\">c) with nominal interest payable yearly&nbsp;into the account at a rate of {int1}%</p>\n<p><em>Recall that if the interest is payable quarterly then the accrued interest is added to the account at the end of each quarter.&nbsp;</em><em>Similarly, if the interest is payable yearly, then the accrued interest is added to the account at the end of each year.</em></p>\n<p>You have &pound;{value} to deposit in a savings account.</p>\n<p>Create a spreadsheet that shows the potential growth of the wealth on&nbsp;each of these accounts over {m} months. The spreadsheet should look&nbsp;similar to:</p>\n<table width=\"624\" height=\"103\" border=\"1\" style=\"height: 103px;\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\">Month</td>\n<td style=\"text-align: center;\">Interest payable monthly</td>\n<td style=\"text-align: center;\">Interest payable quarterly</td>\n<td style=\"text-align: center;\">Interest payable yearly</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">0</td>\n<td style=\"text-align: center;\">{value}</td>\n<td style=\"text-align: center;\">{value}</td>\n<td style=\"text-align: center;\">{value}</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">1</td>\n<td style=\"text-align: center;\">{Month1}</td>\n<td style=\"text-align: center;\">{value}</td>\n<td style=\"text-align: center;\">{value}</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">2</td>\n<td style=\"text-align: center;\">...</td>\n<td style=\"text-align: center;\">...</td>\n<td style=\"text-align: center;\">...</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">...</td>\n<td style=\"text-align: center;\">...</td>\n<td style=\"text-align: center;\">...</td>\n<td style=\"text-align: center;\">...</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">{m}</td>\n<td style=\"text-align: center;\">...</td>\n<td style=\"text-align: center;\">...</td>\n<td style=\"text-align: center;\">...</td>\n</tr>\n</tbody>\n</table>\n<p><em></em></p>\n<p>Click on the button below for hints in Excel.<br/><em></em></p>\n<p><button id=\"#btn\" onclick=\"\n  if (document.getElementById('showhide').style.display == 'block')\n    {document.getElementById('showhide').style.display = 'none';}\n  else\n    {document.getElementById('showhide').style.display = 'block';}\">Hint</button></p>\n<div id=\"showhide\" style=\"display: none;\">\n<ul>\n<li><em>$a^{b+3}$ is written as <strong>a^(b+3)</strong>. </em></li>\n<li><em>Natural logarithm is denoted by <strong>LN(...)</strong>. </em></li>\n<li><em>Recall the difference between a relative reference to a cell <strong>(A3)</strong> and an absolute reference <strong>(A$3$)</strong>. </em></li>\n<li><em>function <strong>FLOOR(x,1)</strong> computes the largest integer smaller than x whilst <strong>CEILING(x,1)</strong> computes the smallest integer larger than x. </em></li>\n<li><em>Google \"Fill formulas into adjacent cells in Excel\" to learn how to avoid manually typing all entries in the table.</em></li>\n</ul>\n</div>", "variable_groups": [{"variables": [], "name": "Unnamed group"}, {"variables": [], "name": "Unnamed group"}], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"growthy": {"definition": "growthy(value,int1,m)", "templateType": "anything", "group": "Ungrouped variables", "name": "growthy", "description": ""}, "interest1": {"definition": "random(0.02..0.04#0.005)", "templateType": "randrange", "group": "Ungrouped variables", "name": "interest1", "description": ""}, "targetm": {"definition": "sum(map(if(s<value1,1,0),s,growthm))-1", "templateType": "anything", "group": "Ungrouped variables", "name": "targetm", "description": ""}, "interest2": {"definition": "{interest1}+0.005", "templateType": "anything", "group": "Ungrouped variables", "name": "interest2", "description": ""}, "growthq": {"definition": "growthq(value,int4,m)", "templateType": "anything", "group": "Ungrouped variables", "name": "growthq", "description": ""}, "growthm": {"definition": "growthm(value,int12,m)", "templateType": "anything", "group": "Ungrouped variables", "name": "growthm", "description": ""}, "targety": {"definition": "sum(map(if(s<value1,1,0),s,growthy))-1", "templateType": "anything", "group": "Ungrouped variables", "name": "targety", "description": ""}, "targetq": {"definition": "sum(map(if(s<value1,1,0),s,growthq))-1", "templateType": "anything", "group": "Ungrouped variables", "name": "targetq", "description": ""}, "sum": {"definition": "{value2}+199", "templateType": "anything", "group": "Ungrouped variables", "name": "sum", "description": ""}, "ceilc": {"definition": "ceil({monthsc}/12)*12", "templateType": "anything", "group": "Ungrouped variables", "name": "ceilc", "description": ""}, "value2": {"definition": "random(5000..10000#100)", "templateType": "randrange", "group": "Ungrouped variables", "name": "value2", "description": ""}, "value1": {"definition": "random({value}+70,{value}+120,{value}+155)", "templateType": "anything", "group": "Ungrouped variables", "name": "value1", "description": ""}, "Month1": {"definition": "precround(growthm[2],2)", "templateType": "anything", "group": "Ungrouped variables", "name": "Month1", "description": ""}, "ceila": {"definition": "ceil({monthsa})", "templateType": "anything", "group": "Ungrouped variables", "name": "ceila", "description": ""}, "ceilb": {"definition": "ceil({monthsb}/3)*3", "templateType": "anything", "group": "Ungrouped variables", "name": "ceilb", "description": ""}, "int12": {"definition": "{int1}-0.1", "templateType": "anything", "group": "Ungrouped variables", "name": "int12", "description": ""}, "int4": {"definition": "{int1}-0.05", "templateType": "anything", "group": "Ungrouped variables", "name": "int4", "description": ""}, "int1": {"definition": "random(4..7#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "int1", "description": ""}, "value": {"definition": "random(400..600#10)", "templateType": "randrange", "group": "Ungrouped variables", "name": "value", "description": ""}, "monthsa": {"definition": "ln({sum}/{value2})/ln(1+({int12}/1200))\n", "templateType": "anything", "group": "Ungrouped variables", "name": "monthsa", "description": ""}, "monthsb": {"definition": "ln({sum}/{value2})/ln(1+({int4}/400))*3", "templateType": "anything", "group": "Ungrouped variables", "name": "monthsb", "description": ""}, "monthsc": {"definition": "ln({sum}/{value2})/ln(1+({int1}/100))*12", "templateType": "anything", "group": "Ungrouped variables", "name": "monthsc", "description": ""}, "ceiltargety": {"definition": "ceil(targety/12)*12", "templateType": "anything", "group": "Ungrouped variables", "name": "ceiltargety", "description": ""}, "m": {"definition": "random(40..60#5)", "templateType": "randrange", "group": "Ungrouped variables", "name": "m", "description": ""}, "ceiltargetq": {"definition": "ceil(targetq/3)*3", "templateType": "anything", "group": "Ungrouped variables", "name": "ceiltargetq", "description": ""}, "ceiltargetm": {"definition": "ceil(targetm)", "templateType": "anything", "group": "Ungrouped variables", "name": "ceiltargetm", "description": ""}}, "metadata": {"notes": "", "description": "", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "James Fung", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/699/"}]}]}], 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