// Numbas version: exam_results_page_options
{"name": "present value - compound interest", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "present value - compound interest", "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>", "advice": "<p>We are asked to find the present&nbsp;value using compound interest. Therefore we will use the equation</p>\n<p>$\\displaystyle P=\\frac{S}{(1+i)^n}$,</p>\n<p>where $S$ is the future value, $P$ is the present value, $i$ is the interest rate per time period and $n$ is the number of time periods.</p>\n<p>In our&nbsp;situation we have,</p>\n<p>$S=\\$\\var{S}$,</p>\n<p>$i=\\frac{\\var{ipa}\\%}{\\var{period[1]}}=\\simplify[unitDenominator]{{ipadec}/{period[1]}}$,</p>\n<p>$n=\\var{years}\\times\\var{period[1]}=\\var{n}$,&nbsp;</p>\n<p>and therefore</p>\n<p>$\\begin{align}P&amp;=\\simplify[simplifyFractions, unitDenominator]{{S}/(1+({ipadec}/{period[1]}))^{n}}\\\\&amp;=\\$ \\var{Prounded} \\text{ &nbsp; &nbsp; &nbsp; &nbsp;(to the nearest cent)}\\end{align}$&nbsp;</p>", "extensions": [], "metadata": {"licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "description": "Using interest compounded at common time intervals (except yearly) determine the present value"}, "variable_groups": [], "functions": {}, "variables": {"years": {"name": "years", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(3..15)"}, "ipa": {"name": "ipa", "templateType": "anything", "description": "<p>interest per annum as a percentage (add the symbol afterwards)</p>", "group": "Ungrouped variables", "definition": "random(1..7#0.1)"}, "n": {"name": "n", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "years*period[1]"}, "ippdec": {"name": "ippdec", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "ipp/100"}, "ipadec": {"name": "ipadec", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "ipa/100"}, "ipp": {"name": "ipp", "templateType": "anything", "description": "<p>interest per period, only use for debugging, use fractions in display and calculations.</p>", "group": "Ungrouped variables", "definition": "ipa/period[1]"}, "P": {"name": "P", "templateType": "anything", "description": "<p>present value</p>", "group": "Ungrouped variables", "definition": "S/(1+ippdec)^n"}, "S": {"name": "S", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(1000..100000#1000)\n"}, "period": {"name": "period", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random([random('half-yearly','semiannually'),2],['quarterly', 4],['monthly',12],['daily', 365])"}, "Prounded": {"name": "Prounded", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "precround(S/(1+ippdec)^n,2)"}}, "tags": [], "parts": [{"variableReplacements": [], "extendBaseMarkingAlgorithm": true, "gaps": [{"variableReplacements": [], "minValue": "P", "precision": "2", "maxValue": "P", "showCorrectAnswer": true, "correctAnswerFraction": false, "mustBeReducedPC": 0, "mustBeReduced": false, "unitTests": [], "precisionType": "dp", "scripts": {}, "extendBaseMarkingAlgorithm": true, "marks": 1, "precisionPartialCredit": 0, "type": "numberentry", "useCustomName": false, "notationStyles": ["plain", "en", "si-en"], "showPrecisionHint": false, "correctAnswerStyle": "plain", "customName": "", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "allowFractions": false, "precisionMessage": "You have not given your answer to the&nbsp;nearest cent.", "customMarkingAlgorithm": "", "strictPrecision": false}], "type": "gapfill", "useCustomName": false, "showCorrectAnswer": true, "customName": "", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "<p>How much would you need to put away at&nbsp;$\\var{ipa}\\%$ per annum compounded {period[0]} in order to have $\\$\\var{S}$ after&nbsp;$\\var{years}$ years?</p>\n<p></p>\n<p>$\\$\\,$[[0]] (to the nearest cent)</p>", "unitTests": [], "sortAnswers": false, "scripts": {}, "customMarkingAlgorithm": "", "marks": 0}], "variablesTest": {"condition": "", "maxRuns": 100}, "preamble": {"js": "", "css": ""}, "rulesets": {}, "ungrouped_variables": ["P", "Prounded", "years", "period", "n", "ipa", "ipadec", "ipp", "ippdec", "S"], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}