// Numbas version: exam_results_page_options
{"name": "Simon's copy of Future Value - Annuity 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"tags": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "statement": "<p><span>To provide for retirement an employee deposits &euro;$\\var{R}$ at the end of each month into an account that earns $\\var{perc}$% annual interest compounded monthly.&nbsp;</span></p>", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>To provide for retirement an employee deposits R&nbsp;at the end of each month in an account that earns $perc% annual interest compound monthly. What is the future value of the annuity in nyears?</p>\n<p>rebelmaths</p>"}, "variable_groups": [], "ungrouped_variables": ["R", "perc", "perc2", "int", "num", "years", "n", "num2", "num3", "A"], "advice": "<p>The future&nbsp;value of an annuity, $A$ is given by:</p>\n<p></p>\n<p>$A=\\frac{R[(1+i)^n-1]}{i}$</p>\n<p>where $R$ represents the periodic payment, $i$ represents the interest rate per period and $n$ represents the number of payments.&nbsp;</p>\n<p></p>\n<p>$A$ represents the future&nbsp;value of the annuity, this is what we are asked&nbsp;to calculate.</p>\n<p>$i$&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 $i=\\frac{\\var{perc2}}{100}=\\var{int}$.</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>$A=\\frac{R[(1+i)^n-1]}{i}$</span></p>\n<p>$A=\\frac{\\var{R}[(1+\\var{int})^{\\var{n}}-1]}{\\var{int}}$</p>\n<p><span>$A=\\frac{\\var{R}[\\var{num}-1]}{\\var{int}}$</span></p>\n<p><span>$A=\\frac{\\var{R}[\\var{num2}]}{\\var{int}}$</span></p>\n<p><span><span><span><span>$A = \\var{R}&nbsp;\\times \\var{num3}$</span></span></span></span></p>\n<p>$A=&pound;\\var{dpformat(A,2)}$ which is $&pound;\\var{dpformat(A,0)}$ to the nearest pound</p>", "extensions": [], "rulesets": {}, "preamble": {"css": "", "js": ""}, "name": "Simon's copy of Future Value - Annuity 1", "parts": [{"showCorrectAnswer": true, "unitTests": [], "marks": 0, "scripts": {}, "gaps": [{"showCorrectAnswer": true, "marks": "3", "scripts": {}, "mustBeReducedPC": 0, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst", "minValue": "A", "useCustomName": false, "precisionType": "dp", "strictPrecision": false, "precisionMessage": "You have not given your answer to the correct precision.", "showPrecisionHint": false, "precision": 0, "unitTests": [], "maxValue": "A", "correctAnswerFraction": false, "allowFractions": false, "customName": "", "precisionPartialCredit": 0, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "type": "numberentry", "customMarkingAlgorithm": "", "correctAnswerStyle": "plain", "showFeedbackIcon": true}], "customName": "", "variableReplacementStrategy": "originalfirst", "useCustomName": false, "showFeedbackIcon": true, "variableReplacements": [], "sortAnswers": false, "type": "gapfill", "extendBaseMarkingAlgorithm": true, "prompt": "<p>What is the future value of the annuity in $\\var{years}$ years?</p>\n<p></p>\n<p>&euro;[[0]]</p>", "customMarkingAlgorithm": ""}], "functions": {}, "variables": {"n": {"name": "n", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "years*12"}, "perc": {"name": "perc", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(4..9#0.5)"}, "num": {"name": "num", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "(1+int)^n"}, "R": {"name": "R", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(50..100#10)"}, "years": {"name": "years", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(5..10)"}, "A": {"name": "A", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "precround(R*num3,2)"}, "num2": {"name": "num2", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "num-1"}, "perc2": {"name": "perc2", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "precround(perc/12,5)"}, "int": {"name": "int", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "perc2/100"}, "num3": {"name": "num3", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "num2/int"}}, "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/"}]}