// Numbas version: exam_results_page_options
{"name": "Practical 2 Q1", "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": "Practical 2 Q1", "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. Alter the number of rows by changing the number next to rows).</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 in annual installments at the end of each year. Assume an interest rate of {interest}%.</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": "Habiba Gora", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/494/"}]}]}], "contributors": [{"name": "Habiba Gora", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/494/"}]}