// Numbas version: finer_feedback_settings
{"name": "future value - annuity due", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "metadata": {"licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "description": "Financial maths. Future value of an annuity due."}, "variables": {"C": {"group": "Ungrouped variables", "name": "C", "description": "", "definition": "if(period[1]=365,random(1..10),random(20..300#10))", "templateType": "anything"}, "F": {"group": "Ungrouped variables", "name": "F", "description": "", "definition": "(C*period[1]/ipadec)*((1+ipadec/period[1])^(n)-1)*(1+ipadec/period[1])", "templateType": "anything"}, "Frounded": {"group": "Ungrouped variables", "name": "Frounded", "description": "", "definition": "precround(F,2)", "templateType": "anything"}, "ipadec": {"group": "Ungrouped variables", "name": "ipadec", "description": "", "definition": "random(0.02..0.10#0.001)", "templateType": "anything"}, "n": {"group": "Ungrouped variables", "name": "n", "description": "", "definition": "years*period[1]", "templateType": "anything"}, "period": {"group": "Ungrouped variables", "name": "period", "description": "", "definition": "random([random('yearly','annually'),1,'year'],[random('half-yearly','semiannually'),2,'half-year'],['quarterly', 4, 'quarter'],['monthly',12,'month'],['daily', 365,'day'])", "templateType": "anything"}, "ipa": {"group": "Ungrouped variables", "name": "ipa", "description": "", "definition": "ipadec*100", "templateType": "anything"}, "years": {"group": "Ungrouped variables", "name": "years", "description": "", "definition": "random(3..20)", "templateType": "anything"}}, "variablesTest": {"maxRuns": 100, "condition": ""}, "ungrouped_variables": ["years", "period", "ipadec", "ipa", "C", "n", "F", "Frounded"], "parts": [{"sortAnswers": false, "unitTests": [], "marks": 0, "prompt": "<p>Suppose you are given $\\$\\var{C}$&nbsp;at the beginning&nbsp;of each&nbsp;{period[2]}&nbsp;for $\\var{years}$&nbsp;years. If the interest rate is $\\var{ipa}\\%$ per annum compounding {period[0]}, what is this cash flow worth at the end&nbsp;of the $\\var{years}$&nbsp;years?</p>\n<p></p>\n<p>$\\$$&nbsp;[[0]] (to the nearest cent)</p>", "customName": "", "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "useCustomName": false, "type": "gapfill", "scripts": {}, "gaps": [{"maxValue": "F", "precision": "2", "unitTests": [], "showCorrectAnswer": true, "precisionType": "dp", "strictPrecision": true, "showPrecisionHint": false, "mustBeReduced": false, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "useCustomName": false, "allowFractions": false, "customName": "", "notationStyles": ["plain", "en", "si-en"], "precisionMessage": "You have not given your answer to the nearest cent.", "mustBeReducedPC": 0, "marks": 1, "correctAnswerStyle": "plain", "minValue": "F", "showFeedbackIcon": true, "variableReplacements": [], "correctAnswerFraction": false, "type": "numberentry", "scripts": {}, "precisionPartialCredit": 0, "customMarkingAlgorithm": ""}]}], "preamble": {"js": "", "css": ""}, "name": "future value - annuity due", "advice": "<p>You are asked to find the future&nbsp;value of an annuity due (since the payments are at the start&nbsp;of each&nbsp;period). Therefore we will use the future value of an annuity due formula</p>\n<p>$\\displaystyle F=\\frac{C}{i}\\left((1+i)^n-1\\right)(1+i)$</p>\n<p>where $F$ is the future&nbsp;value, $C$ is the cash flow per period, $i$ is the interest rate per period, and $n$ is the number of periods.</p>\n<p>In our&nbsp;situation we have,</p>\n<p>$C=\\var{C}$,</p>\n<p><span data-jme-visible=\"period[1]&gt;1\">$i=\\frac{\\var{ipa}\\%}{\\var{period[1]}}=\\frac{\\var{ipadec}}{\\var{period[1]}}$,</span> <span data-jme-visible=\"period[1]=1\">$i=\\var{ipa}\\%=\\var{ipadec}$,</span></p>\n<p><span data-jme-visible=\"period[1]&gt;1\">$n=\\var{years}\\times \\var{period[1]}=\\var{n}$,</span> <span data-jme-visible=\"period[1]=1\">$n=\\var{n}$,</span></p>\n<p>and therefore we have</p>\n<p>$\\displaystyle F=\\frac{\\var{C}}{\\left(\\simplify[unitDenominator]{{ipadec}/{period[1]}}\\right)}\\left(\\left(1+\\simplify[unitDenominator]{{ipadec}/{period[1]}}\\right)^\\var{n}-1\\right)\\left(1+\\simplify[unitDenominator]{{ipadec}/{period[1]}}\\right)$</p>\n<p>Calculating this we find&nbsp;</p>\n<p>$\\begin{align}F&amp;\\approx \\var{F}\\\\&amp;=\\$\\var{Frounded}\\quad \\text{(to the nearest cent)}\\end{align}$</p>", "statement": "<p>If you are unsure of how to do&nbsp;a question, click on&nbsp;<em>Reveal answers</em>&nbsp;to see the full working. Then, once you understand how to do the question, click on&nbsp;<em>Try another question like this one</em>&nbsp;to start again. Do each question repeatedly to ensure you have mastered it.</p>", "functions": {}, "tags": [], "rulesets": {}, "extensions": [], "type": "question", "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}