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{"name": "Savings compound interest 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variables": {"ratio": {"name": "ratio", "group": "Ungrouped variables", "definition": "A/P", "description": "", "templateType": "anything"}, "perc": {"name": "perc", "group": "Ungrouped variables", "definition": "random(1.5..5.5 #0.5)", "description": "", "templateType": "anything"}, "A": {"name": "A", "group": "Ungrouped variables", "definition": "precround(P*(1+int)^n,2)", "description": "", "templateType": "anything"}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "random(2..6 #1)", "description": "", "templateType": "anything"}, "intplus": {"name": "intplus", "group": "Ungrouped variables", "definition": "ratio^(1/n)", "description": "", "templateType": "anything"}, "int": {"name": "int", "group": "Ungrouped variables", "definition": "perc/100", "description": "", "templateType": "anything"}, "P": {"name": "P", "group": "Ungrouped variables", "definition": "random(1000..6000 #500)", "description": "", "templateType": "anything"}}, "rulesets": {}, "showQuestionGroupNames": false, "ungrouped_variables": ["n", "P", "A", "perc", "int", "ratio", "intplus"], "variablesTest": {"condition": "", "maxRuns": 100}, "extensions": [], "name": "Savings compound interest 2", "parts": [{"prompt": "<p><span>What is the value of </span><em><strong>P</strong></em><span>?</span></p>\n<p><span>&euro;[[0]]</span></p>", "gaps": [{"allowFractions": false, "correctAnswerFraction": false, "showPrecisionHint": false, "maxValue": "P+0.0001", "scripts": {}, "variableReplacementStrategy": "originalfirst", "minValue": "P-0.0001", "variableReplacements": [], "marks": 1, "type": "numberentry", "showCorrectAnswer": true}], "scripts": {}, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0, "type": "gapfill", "showCorrectAnswer": true}, {"prompt": "<p><span>What is the value of <em><strong>A</strong></em></span><span>?</span></p>\n<p><span>&euro;[[0]]</span></p>", "gaps": [{"allowFractions": false, "correctAnswerFraction": false, "showPrecisionHint": false, "maxValue": "A+0.0001", "scripts": {}, "variableReplacementStrategy": "originalfirst", "minValue": "A-0.0001", "variableReplacements": [], "marks": 1, "type": "numberentry", "showCorrectAnswer": true}], "scripts": {}, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0, "type": "gapfill", "showCorrectAnswer": true}, {"prompt": "<p><span>What is the value of <em><strong>n</strong></em></span><span>?</span></p>\n<p><span></span></p>\n<p><span>[[0]]</span></p>", "gaps": [{"allowFractions": false, "correctAnswerFraction": false, "showPrecisionHint": false, "maxValue": "n+0.0001", "scripts": {}, "variableReplacementStrategy": "originalfirst", "minValue": "n-0.0001", "variableReplacements": [], "marks": 1, "type": "numberentry", "showCorrectAnswer": true}], "scripts": {}, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0, "type": "gapfill", "showCorrectAnswer": true}, {"prompt": "<p>What is the interest rate per annum?</p>\n<p>Please give your answer as a <strong>percentage</strong>&nbsp;correct to 2 decimal places.</p>\n<p></p>\n<p>[[0]]%</p>", "gaps": [{"allowFractions": false, "correctAnswerFraction": false, "showPrecisionHint": false, "maxValue": "perc+0.02", "scripts": {}, "variableReplacementStrategy": "originalfirst", "minValue": "perc-0.02", "variableReplacements": [], "marks": "3", "type": "numberentry", "showCorrectAnswer": true}], "scripts": {}, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0, "type": "gapfill", "showCorrectAnswer": true}], "question_groups": [{"name": "", "pickQuestions": 0, "pickingStrategy": "all-ordered", "questions": []}], "variable_groups": [], "advice": "<p><span>The compound interest formula is: $\\ A = P(1+i)^n $</span></p>\n<p><strong>Part (a)</strong></p>\n<p><em><strong>P</strong></em> represents the principal sum invested , so in this example it is &euro;$\\var{P}$.</p>\n<p><strong>Part (b)</strong></p>\n<p><span><em><strong>A</strong></em>&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>Part (c)</strong></p>\n<p><em><strong>n</strong></em>&nbsp;represents the number of compounding periods&nbsp;, so in this example it is $\\var{n}$ years.</p>\n<p><strong>Part(d)</strong></p>\n<p><span>Using the compound interest formula:</span></p>\n<p><span>$A=P(1+i)^n$</span></p>\n<p><span>$\\var{A}=\\var{P}(1+i)^\\var{n}$</span></p>\n<p><span>We need to rearrange the equation to find the value of $i$.</span></p>\n<p><span>$\\frac{\\var{A}}{\\var{P}}=(1+i)^\\var{n}$</span></p>\n<p><span>$\\var{ratio}=(1+i)^\\var{n}$</span></p>\n<p><span>$\\sqrt[\\var{n}]{\\var{ratio}}=1+i$</span></p>\n<p><span>$\\var{intplus}=1+i$</span></p>\n<p>$i=\\var{int}$ so the annual interest rate is $\\var{perc}$%.</p>", "metadata": {"description": "<p>Calculate the annual interest rate for a savings account where A, P and n are given.</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "preamble": {"css": "", "js": ""}, "tags": ["rebel", "Rebel", "REBEL", "rebelmaths"], "functions": {}, "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+i)^n $</p>", "type": "question", "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}]}], "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}