// Numbas version: exam_results_page_options
{"name": "future value - compound interest (annual only)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"metadata": {"description": "Using interest compounded annually determine the future value", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "variables": {"ipa": {"description": "<p>interest per annum as a percentage (add the symbol afterwards)</p>", "templateType": "anything", "definition": "random(1..7#0.1)", "name": "ipa", "group": "Ungrouped variables"}, "ippdec": {"description": "", "templateType": "anything", "definition": "ipp/100", "name": "ippdec", "group": "Ungrouped variables"}, "P": {"description": "<p>present value</p>", "templateType": "anything", "definition": "random(1000..100000#1000)", "name": "P", "group": "Ungrouped variables"}, "n": {"description": "", "templateType": "anything", "definition": "years*period[1]", "name": "n", "group": "Ungrouped variables"}, "ipadec": {"description": "", "templateType": "anything", "definition": "ipa/100", "name": "ipadec", "group": "Ungrouped variables"}, "ipp": {"description": "<p>interest per period, only use for debugging, use fractions in display and calculations.</p>", "templateType": "anything", "definition": "ipa/period[1]", "name": "ipp", "group": "Ungrouped variables"}, "S": {"description": "", "templateType": "anything", "definition": "P*(1+(ipadec/period[1]))^n", "name": "S", "group": "Ungrouped variables"}, "years": {"description": "", "templateType": "anything", "definition": "random(3..15)", "name": "years", "group": "Ungrouped variables"}, "Srounded": {"description": "", "templateType": "anything", "definition": "precround((P*(1+ippdec)^n,2))", "name": "Srounded", "group": "Ungrouped variables"}, "period": {"description": "", "templateType": "anything", "definition": "[random('yearly','annually'),1]", "name": "period", "group": "Ungrouped variables"}}, "variable_groups": [], "tags": [], "advice": "<p>We are asked to find the future value using compound interest. Therefore we will use the equation</p>\n<p>$S=P(1+i)^n$,</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>$P=\\$\\var{P}$,</p>\n<p>$i=\\var{ipa}\\%=\\var{ipadec}$,</p>\n<p>$n=\\var{years}$,&nbsp;</p>\n<p>and therefore</p>\n<p>$\\begin{align}S&amp;=\\var{P}\\left(1+\\var{ipadec}\\right)^\\var{n}\\\\&amp;=\\$ \\var{Srounded} \\text{ &nbsp; &nbsp; &nbsp; &nbsp;(to the nearest cent)}\\end{align}$&nbsp;</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>", "preamble": {"js": "", "css": ""}, "name": "future value - compound interest (annual only)", "rulesets": {}, "extensions": [], "functions": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["P", "years", "period", "n", "ipa", "ipadec", "ipp", "ippdec", "S", "Srounded"], "parts": [{"showFeedbackIcon": true, "gaps": [{"showPrecisionHint": false, "precisionMessage": "You have not given your answer to the&nbsp;nearest cent.", "mustBeReducedPC": 0, "allowFractions": false, "marks": 1, "minValue": "S", "strictPrecision": false, "notationStyles": ["plain", "en", "si-en"], "useCustomName": false, "unitTests": [], "customName": "", "variableReplacements": [], "precision": "2", "correctAnswerStyle": "plain", "precisionPartialCredit": 0, "precisionType": "dp", "showFeedbackIcon": true, "type": "numberentry", "customMarkingAlgorithm": "", "mustBeReduced": false, "variableReplacementStrategy": "originalfirst", "maxValue": "S", "scripts": {}, "extendBaseMarkingAlgorithm": true, "correctAnswerFraction": false, "showCorrectAnswer": true}], "type": "gapfill", "prompt": "<p>If a bank account has&nbsp;a balance of $\\$\\var{P}$&nbsp;and it earns $\\var{ipa}\\%$ per annum compounded {period[0]}, what will be the balance of&nbsp;the account after $\\var{years}$ years? &nbsp;</p>\n<p></p>\n<p>$\\$\\,$[[0]] (to the nearest cent)</p>", "customMarkingAlgorithm": "", "marks": 0, "useCustomName": false, "scripts": {}, "unitTests": [], "customName": "", "variableReplacements": [], "sortAnswers": false, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true}], "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/"}]}