// Numbas version: finer_feedback_settings
{"name": "Simon's copy of Savings compound interest 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Calculate the annual interest rate for a savings account where A, P and n are given.</p>\n<p>rebelmaths</p>"}, "ungrouped_variables": ["n", "P", "A", "perc", "int", "ratio", "intplus"], "variablesTest": {"maxRuns": 100, "condition": ""}, "variable_groups": [], "functions": {}, "advice": "<p><span>The compound interest formula is: $\\ A = P(1+r)^n $</span></p>\n<p><strong></strong></p>\n<p><strong>(a)</strong></p>\n<p>$P$ represents the principal sum invested, so in this example it is &euro;$\\var{P}$.</p>\n<p><strong></strong></p>\n<p><strong>(b)</strong></p>\n<p><span>$A$&nbsp;represents the amount in the&nbsp;<span>deposit account after $\\var{n}$ years, so in this example&nbsp;it is &euro;$\\var{A}$</span>.</span></p>\n<p><strong></strong></p>\n<p><strong>(c)</strong></p>\n<p>$n$ represents the number of compounding periods, so in this example it is $\\var{n}$ years.</p>\n<p><strong></strong></p>\n<p><strong>(d)</strong></p>\n<p><span>Using the compound interest formula:</span></p>\n<p><span>$A=P(1+r)^n$</span></p>\n<p><span>$\\var{A}=\\var{P}(1+r)^\\var{n}$</span></p>\n<p><span>We need to rearrange the equation to find the value of $r$.</span></p>\n<p><span>$\\frac{\\var{A}}{\\var{P}}=(1+r)^\\var{n}$</span></p>\n<p><span>$\\var{ratio}=(1+r)^\\var{n}$</span></p>\n<p><span>$\\sqrt[\\var{n}]{\\var{ratio}}=1+r$</span></p>\n<p><span>$\\var{intplus}=1+r$</span></p>\n<p>$r=\\var{int}$ so multiplying by 100 gives the annual interest rate as a percentage is $\\var{perc}$%.</p>", "statement": "<p>A lump sum of &euro;$\\var{P}$ is deposited into a savings account that pays compound interest for $\\var{n}$ years. If no withdrawals are made from the account, then the amount that the lump sum will have grown to is &euro;$\\var{A}$.</p>\n<p>The compound interest formula is:</p>\n<p>$\\ A = P(1+r)^n $</p>", "parts": [{"useCustomName": false, "sortAnswers": false, "marks": 0, "customMarkingAlgorithm": "", "scripts": {}, "customName": "", "prompt": "<p>What is the value of $P$?</p>\n<p><span>&euro;[[0]]</span></p>", "showFeedbackIcon": true, "gaps": [{"useCustomName": false, "allowFractions": false, "minValue": "P", "marks": 1, "customMarkingAlgorithm": "", "scripts": {}, "maxValue": "P", "customName": "", "showFractionHint": true, "showFeedbackIcon": true, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "showCorrectAnswer": true, "correctAnswerFraction": false, "unitTests": [], "variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "type": "numberentry", "mustBeReducedPC": 0}], "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "showCorrectAnswer": true, "unitTests": [], "variableReplacementStrategy": "originalfirst", "type": "gapfill"}, {"useCustomName": false, "sortAnswers": false, "marks": 0, "customMarkingAlgorithm": "", "scripts": {}, "customName": "", "prompt": "<p>What is the value of $A$?</p>\n<p><span>&euro;[[0]]</span></p>", "showFeedbackIcon": true, "gaps": [{"useCustomName": false, "allowFractions": false, "minValue": "A", "marks": 1, "customMarkingAlgorithm": "", "scripts": {}, "maxValue": "A", "customName": "", "showFractionHint": true, "showFeedbackIcon": true, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "showCorrectAnswer": true, "correctAnswerFraction": false, "unitTests": [], "variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "type": "numberentry", "mustBeReducedPC": 0}], "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "showCorrectAnswer": true, "unitTests": [], "variableReplacementStrategy": "originalfirst", "type": "gapfill"}, {"useCustomName": false, "sortAnswers": false, "marks": 0, "customMarkingAlgorithm": "", "scripts": {}, "customName": "", "prompt": "<p>What is the value of $n$?</p>\n<p><span></span></p>\n<p><span>[[0]]</span></p>", "showFeedbackIcon": true, "gaps": [{"useCustomName": false, "allowFractions": false, "minValue": "n", "marks": 1, "customMarkingAlgorithm": "", "scripts": {}, "maxValue": "n", "customName": "", "showFractionHint": true, "showFeedbackIcon": true, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "showCorrectAnswer": true, "correctAnswerFraction": false, "unitTests": [], "variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "type": "numberentry", "mustBeReducedPC": 0}], "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "showCorrectAnswer": true, "unitTests": [], "variableReplacementStrategy": "originalfirst", "type": "gapfill"}, {"useCustomName": false, "sortAnswers": false, "marks": 0, "customMarkingAlgorithm": "", "scripts": {}, "customName": "", "prompt": "<p>What is the interest rate per annum?</p>\n<p>Please give your answer as a <strong>percentage</strong>&nbsp;correct to&nbsp;1 decimal place.</p>\n<p></p>\n<p>[[0]]%</p>", "showFeedbackIcon": true, "gaps": [{"customMarkingAlgorithm": "", "customName": "", "showPrecisionHint": false, "marks": "3", "notationStyles": ["plain", "en", "si-en"], "minValue": "perc", "precisionPartialCredit": 0, "mustBeReduced": false, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "useCustomName": false, "allowFractions": false, "scripts": {}, "maxValue": "perc", "precisionMessage": "You have not given your answer to the correct precision.", "precision": "1", "showFeedbackIcon": true, "precisionType": "dp", "correctAnswerFraction": false, "strictPrecision": false, "unitTests": [], "correctAnswerStyle": "plain", "type": "numberentry"}], "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "showCorrectAnswer": true, "unitTests": [], "variableReplacementStrategy": "originalfirst", "type": "gapfill"}], "tags": [], "variables": {"perc": {"name": "perc", "definition": "random(1.5..5.5 #0.1)", "templateType": "anything", "description": "", "group": "Ungrouped variables"}, "int": {"name": "int", "definition": "perc/100", "templateType": "anything", "description": "", "group": "Ungrouped variables"}, "n": {"name": "n", "definition": "random(2..6 #1)", "templateType": "anything", "description": "", "group": "Ungrouped variables"}, "intplus": {"name": "intplus", "definition": "ratio^(1/n)", "templateType": "anything", "description": "", "group": "Ungrouped variables"}, "P": {"name": "P", "definition": "random(1000..6000 #500)", "templateType": "anything", "description": "", "group": "Ungrouped variables"}, "ratio": {"name": "ratio", "definition": "A/P", "templateType": "anything", "description": "", "group": "Ungrouped variables"}, "A": {"name": "A", "definition": "precround(P*(1+int)^n,2)", "templateType": "anything", "description": "", "group": "Ungrouped variables"}}, "name": "Simon's copy of Savings compound interest 2", "rulesets": {}, "preamble": {"css": "", "js": ""}, "extensions": [], "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/"}]}