// Numbas version: finer_feedback_settings
{"name": "MATH1510 Financial Mathematics 1 Practical 2A", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {"balances": {"definition": "var cells = [[0,0,0,0,value]];\nvar repayment = (value)/((p)*(an));\n\nfor (i=0; i < n; i++) {\n  var tobank;\n  if (i <= n) {tobank = repayment;}\n  else {tobank = 0;}\n  var interest = intdec*cells[i][4];\n  var payment = repayment - interest;\n  var obalance = cells[i][4] - payment;\n  \n  cells.push([i+1,tobank,interest,payment,obalance]);\n}\n\nreturn cells;", "type": "list", "parameters": [["an", "number"], ["intdec", "number"], ["n", "number"], ["p", "number"], ["value", "number"]], "language": "javascript"}}, "ungrouped_variables": ["value", "p", "n", "interest", "intdec", "v", "an", "repayment", "balance", "sheet"], "name": "MATH1510 Financial Mathematics 1 Practical 2A", "tags": [], "advice": "<p style=\"text-align: left;\">A loan&nbsp;scehdule can be used to determine the outstanding balance of a loan. A loan&nbsp;schedule consists of two components:</p>\n<ol>\n<li>interest component</li>\n<li>repayment component</li>\n</ol>\n<ul>\n<li><b>Payments</b></li>\n</ul>\n<p>The total number of payments is the number of payments in one year multiplied by the number of years.</p>\n<p style=\"text-align: center;\">total number of payments= $np$</p>\n<p style=\"text-align: left;\">where:</p>\n<ul>\n<li>$n$= the number of years of the loan</li>\n<li>$p$= number of periods in a year</li>\n</ul>\n<p>In the above question, substituting in $n$={n} and $p$={p} will give the total number of payments.</p>\n<ul>\n<li><strong>Payment every period</strong></li>\n</ul>\n<p>As we know the value of the loan&nbsp;and that the repayment each period is like an annuity, we know that the present value of the annuity&nbsp;multipled by the number of periods in a year will give the value of the loan&nbsp;(see Numbas- Annuities PV).</p>\n<p style=\"text-align: center;\">$px{a}_{n|}^{p}=loan$</p>\n<p style=\"text-align: left;\">where:</p>\n<ul>\n<li>$p$= number of periods in one year</li>\n<li>${a}_{n|}^{p}$= present value of a standard annuity&nbsp;paying p times a year for n years with payments of $1 \\over p$ each&nbsp;period</li>\n<li>$x$= payment every period</li>\n</ul>\n<p>Re-arranging the above:</p>\n<p style=\"text-align: center;\"><span>$x={loan \\over p{a}_{n|}^{p}}$</span></p>\n<p style=\"text-align: left;\"><span>In the above question, working out ${a}_{n|}^{p}$ with an&nbsp;effective interest rate&nbsp;of {interest}% and substituting in loan=&pound;{value} and $p$={p} will give the value of each payment.</span></p>\n<ul>\n<li><strong>Interest component</strong></li>\n</ul>\n<p style=\"text-align: center;\">$i$*OB of previous year</p>\n<ul>\n<li><strong>Repayment component</strong></li>\n</ul>\n<p style=\"text-align: center;\">Annual payment - interest component</p>\n<ul>\n<li><strong>Outstanding balance</strong></li>\n</ul>\n<p style=\"text-align: center;\">OB of previous year - repayment component of current year</p>", "rulesets": {}, "parts": [{"precisionType": "dp", "prompt": "<p>What is the value (to two decimal places) of each payment?</p>", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "{repayment}", "minValue": "{repayment}", "variableReplacementStrategy": "originalfirst", "strictPrecision": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "scripts": {}, "marks": "5", "type": "numberentry", "showPrecisionHint": false}, {"scripts": {}, "precisionType": "dp", "numColumns": "5", "prompt": "<p>Create a table in Excel presenting a loan schedule showing the interest and repayment component of every payment and the outstanding balance. Each entry should be to two decimal places.</p>\n<p><em>(Let the first column be the year, second column annual payment, third column interest component, fourth column repayment component and the fifth column outstanding balance.</em></p>\n<p><em><strong>Alter the number of rows by changing the number next to rows and begin the first row with year 1</strong>)</em></p>\n<p>Click on the button below for hints on Excel functions.<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>The function&nbsp;<strong>=PMT(rate,nper,fv,type)&nbsp;</strong>calculates the repayment per period for a loan based on a constant period and interest rate. Note: these payments are per period, so if the payments are, for example, monthly we need to use the specific interest rate $i_{[12]}$.</li>\n<li>The function =<strong>IPMT(rate,per,nper,pv,fv,type)</strong> calculates the amount of each payment which goes towards paying off the interest of loan in any specific period, where the period is specified by the '<em>per</em>' argument and this ranges from 1 to <em>nper</em>.&nbsp;</li>\n<li>The function&nbsp;<strong>=PPMT(rate,per,nper,pv,fv,type)</strong> calculates the amount of each payment which goes towards paying off the principal of loan in any specific period, where the period if specified by the '<em>per</em>' argument and this ranges from 1 to&nbsp;<em>nper</em>.</li>\n<li>For more information on these functions and more financial commands, see:&nbsp;<a href=\"https://support.office.com/en-us/article/Financial-functions-reference--5658d81e-6035-4f24-89c1-fbf124c2b1d8?CorrelationId=d4068026-9b57-4e03-9359-aa6a3cb14f9a&amp;ui=en-US&amp;rs=en-US&amp;ad=US\">Financial Functions in Excel</a>.</li>\n</ul>\n</div>", "variableReplacementStrategy": "originalfirst", "type": "matrix", "precisionMessage": "<p>You have not given your answer to two decimal places.</p>", "allowFractions": false, "variableReplacements": [], "precision": "2", "markPerCell": true, "numRows": "1", "strictPrecision": false, "tolerance": 0, "showCorrectAnswer": true, "correctAnswer": "sheet", "precisionPartialCredit": "50", "correctAnswerFractions": false, "marks": "20", "allowResize": true}], "statement": "<p>A {n} year loan of &pound;{value} is to be repaid by equal annual installments at the end of each year. Assume an annual effective interest rate of {interest}% p.a.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"balance": {"definition": "balances(an,intdec,n,p,value)", "templateType": "anything", "group": "Ungrouped variables", "name": "balance", "description": ""}, "sheet": {"definition": "matrix(balance[1..n+1])", "templateType": "anything", "group": "Ungrouped variables", "name": "sheet", "description": ""}, "repayment": {"definition": "{value}/({p}*{an})", "templateType": "anything", "group": "Ungrouped variables", "name": "repayment", "description": ""}, "value": {"definition": "random(1000..5000#500)", "templateType": "randrange", "group": "Ungrouped variables", "name": "value", "description": ""}, "n": {"definition": "random(4..6#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "n", "description": ""}, "p": {"definition": "1", "templateType": "number", "group": "Ungrouped variables", "name": "p", "description": ""}, "interest": {"definition": "5", "templateType": "number", "group": "Ungrouped variables", "name": "interest", "description": ""}, "v": {"definition": "1/(1+{intdec})", "templateType": "anything", "group": "Ungrouped variables", "name": "v", "description": ""}, "an": {"definition": "(1-({v}^{n}))/{intdec}", "templateType": "anything", "group": "Ungrouped variables", "name": "an", "description": ""}, "intdec": {"definition": "{interest}/100", "templateType": "anything", "group": "Ungrouped variables", "name": "intdec", "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/"}]}]}], "contributors": [{"name": "James Fung", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/699/"}]}