// Numbas version: exam_results_page_options
{"name": "Simon's copy of Present value - Annuity 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"parts": [{"showFeedbackIcon": true, "variableReplacements": [], "gaps": [{"showFeedbackIcon": true, "precisionMessage": "You have not given your answer to the correct precision.", "customMarkingAlgorithm": "", "correctAnswerStyle": "plain", "strictPrecision": true, "correctAnswerFraction": false, "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "maxValue": "P+0.01", "allowFractions": false, "variableReplacementStrategy": "originalfirst", "unitTests": [], "precision": "2", "marks": "5", "minValue": "P-0.01", "variableReplacements": [], "precisionType": "dp", "extendBaseMarkingAlgorithm": true, "customName": "", "scripts": {}, "type": "numberentry", "showPrecisionHint": false, "mustBeReduced": false, "useCustomName": false, "showCorrectAnswer": true, "precisionPartialCredit": 0}], "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "customName": "", "sortAnswers": false, "showCorrectAnswer": true, "scripts": {}, "prompt": "<p>Find the present value of these payments if the annual interest rate is $\\var{perc}$% compounded monthly. Give your answer to the nearest cent.</p>\n<p>&euro;[[0]]</p>", "variableReplacementStrategy": "originalfirst", "unitTests": [], "useCustomName": false, "marks": 0, "type": "gapfill"}], "functions": {}, "name": "Simon's copy of Present value - Annuity 2", "tags": [], "extensions": [], "variablesTest": {"condition": "", "maxRuns": 100}, "variable_groups": [{"variables": [], "name": "Unnamed group"}], "ungrouped_variables": ["perc", "int", "P", "n", "R", "Interest", "num", "perc2", "num2", "num3", "years"], "variables": {"perc2": {"definition": "precround(perc/12, 5)", "group": "Ungrouped variables", "description": "", "name": "perc2", "templateType": "anything"}, "perc": {"definition": "random(4.5..8.5#0.5)", "group": "Ungrouped variables", "description": "", "name": "perc", "templateType": "anything"}, "P": {"definition": "precround(R*((1-(1+int)^(-n))/int),2)", "group": "Ungrouped variables", "description": "", "name": "P", "templateType": "anything"}, "years": {"definition": "random(1..3)", "group": "Ungrouped variables", "description": "", "name": "years", "templateType": "anything"}, "R": {"definition": "random(280..400 # 10)", "group": "Ungrouped variables", "description": "", "name": "R", "templateType": "anything"}, "num2": {"definition": "1-num", "group": "Ungrouped variables", "description": "", "name": "num2", "templateType": "anything"}, "Interest": {"definition": "n*R-P", "group": "Ungrouped variables", "description": "", "name": "Interest", "templateType": "anything"}, "int": {"definition": "perc2/100", "group": "Ungrouped variables", "description": "", "name": "int", "templateType": "anything"}, "num": {"definition": "(1+int)^-n", "group": "Ungrouped variables", "description": "", "name": "num", "templateType": "anything"}, "num3": {"definition": "num2/int", "group": "Ungrouped variables", "description": "", "name": "num3", "templateType": "anything"}, "n": {"definition": "years*12", "group": "Ungrouped variables", "description": "", "name": "n", "templateType": "anything"}}, "rulesets": {}, "preamble": {"css": "", "js": ""}, "advice": "<p>The present value of an annuity, $P$ is given by:</p>\n<p></p>\n<p>$P=\\frac{R[1-(1+r)^{-n}]}{r}$</p>\n<p>where $R$ represents the periodic payment, $r$ represents the interest rate per period and $n$ represents the number of payments.&nbsp;</p>\n<p></p>\n<p>$P$ represents the present value of the annuity, this is what we are asked&nbsp;to calculate.</p>\n<p>$r$&nbsp;represents the rate of compound interest. the annual interest rate is $\\var{perc}$% so the monthly rate of interest is $\\frac {\\var{perc}} {12}=\\var{perc2}$% and therefore $r=\\frac{\\var{perc2}}{100}=\\var{int}$.</p>\n<p>$n$<b><i>&nbsp;</i></b>represents the number of payments, there are 12 payments over $\\var{years}$ year(s) so $n$ is $12 \\times \\var{years}=\\var{n}$.</p>\n<p>The value of each repayment, is &euro;$\\var{R}$&nbsp;</p>\n<p></p>\n<p>Using the formula:</p>\n<p><span>$P=\\frac{R[1-(1+r)^{-n}]}{r}$</span></p>\n<p>$P=\\frac{\\var{R}[1-(1+\\var{int})^{-\\var{n}}]}{\\var{int}}$</p>\n<p><span>$P=\\frac{\\var{R}[1-\\var{num}]}{\\var{int}}$</span></p>\n<p><span>$P=\\frac{\\var{R}[\\var{num2}]}{\\var{int}}$</span></p>\n<p><span><span><span><span>$P = \\var{R}&nbsp;\\times \\var{num3}$</span></span></span></span></p>\n<p>$P=\\var{P}$</p>\n<p></p>", "metadata": {"description": "<p>A 1-year lease for a company car requires a payment of &euro;280 at the end of each month. Find the present value of these payments if the annual interest rate is 7% compounded monthly.</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>A $\\var{years}$-year lease for a company car requires a payment of &euro;$\\var{R}$&nbsp;at the end of each month.&nbsp;</p>\n<p></p>\n<p>The formula for calculating the present value ($P$) of an annuity is:</p>\n<p>$P=\\frac{R[1-(1+r)^{-n}]}{r}$</p>\n<p>where $R$ represents the value of each&nbsp;repayment, $r$ represents the interest rate and $n$ represents the number repayments.</p>\n<p></p>", "type": "question", "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}]}], "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}