// Numbas version: exam_results_page_options
{"name": "Savings compound interest 3", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["perc1", "perc2", "int1", "int2", "n1", "n2", "P", "A1", "A2", "int3"], "name": "Savings compound interest 3", "tags": ["compound interest", "rebel", "REBEL", "Rebel", "rebelmaths"], "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>n</strong></em>&nbsp;represents the number of compounding periods&nbsp;, so for Bank A&nbsp;it is $\\var{n1}$ years.</p>\n<p><span><em><strong>i</strong></em></span><span>&nbsp;represents the rate of compound interest, for Bank A, the annual interest rate is $\\var{perc1}$% so <em><strong>i</strong></em> is $\\frac {\\var{perc1}} {100}=\\var{int1}$.</span></p>\n<p>The total amount saved after<span>&nbsp;$\\var{n1}$ years is denoted by <em><strong>A</strong></em>. Using the compound interest formula:</span></p>\n<p><span>$A=P(1+i)^n$</span></p>\n<p><span>$A=\\var{P} \\times(1+\\var{int1})^\\var{n1}=\\var{A1}$</span></p>\n<p><strong>Part(b)</strong></p>\n<p><em><strong>n</strong></em>&nbsp;represents the number of compounding periods. For Bank B, i<span>nterest is compounded daily&nbsp;for $\\var{n1}$ years so there are a total of $365 \\times \\var{n1} =\\var{n2}$ compounding periods.</span></p>\n<p><span><em><strong>i</strong></em></span><span>&nbsp;represents the rate of compound interest.&nbsp;For Bank B,&nbsp;</span>the interest rate is ${\\var{perc2}}$% per annum compounded daily.</p>\n<p>The interest rate per day&nbsp;is $\\frac{\\var{perc2}}{365}=\\var{int3}$%</p>\n<p>Therefore $i=\\frac{\\var{int3}}{100}=\\var{int2}$</p>\n<p>The amount <span>saved</span><span>&nbsp;after $\\var{n1}$ years is denoted by <em><strong>A</strong></em>. Using the compound interest formula:</span></p>\n<p><span>$A=P(1+i)^n$</span></p>\n<p><span>$A=\\var{P} \\times(1+\\var{int2})^\\var{n2}=\\var{A2}$</span></p>", "rulesets": {}, "parts": [{"prompt": "<p>Suppose that the potential customer chooses Bank A.</p>\n<p>What is the value of $n$?</p>\n<p>[[0]]</p>\n<p>What is the value of $i$?</p>\n<p>[[1]]</p>\n<p>What is the value of $A$? &nbsp;Please give your answer to the nearest cent.</p>\n<p>&euro;[[2]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "n1+0.00001", "minValue": "n1-0.00001", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "int1+0.0001", "minValue": "int1-0.0001", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "A1+0.01", "minValue": "A1-0.01", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>Suppose that the potential customer chooses Bank B.</p>\n<p><span>What is the value of $n$? &nbsp;</span></p>\n<p>[[0]]</p>\n<p>What is the value of $i$? &nbsp;Please include all the&nbsp;decimal places in your answer.</p>\n<p>[[1]]</p>\n<p></p>\n<p>What is the value of $A$? &nbsp;Please give your answer to the nearest cent.</p>\n<p>&euro;[[2]]</p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "n2+0.00001", "minValue": "n2-0.00001", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "int2+0.00001", "minValue": "int2-0.00001", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "A2+0.05", "minValue": "A2-0.05", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "<p>Two rival high street banks offer customers a new deposit&nbsp;account.</p>\n<p>Bank A offers an account that earns interest at a rate of $\\var{perc1}$% per annum&nbsp;where interest is compounded annually.</p>\n<p>Bank B <span>offers an account that earns interest at a nominal rate of $\\var{perc2}$% per annum&nbsp;where interest is compounded daily. </span></p>\n<p>Suppose that a potential customer has &euro;$\\var{P}$ to invest for $\\var{n1}$ years. &nbsp; &nbsp;</p>\n<p>The compound interest formula is:</p>\n<p>$\\ A = P(1+i)^n $</p>\n<p></p>\n<p><span>You may assume that there are 365 days per annum.</span></p>\n<p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"A1": {"definition": "precround(P*(1+int1)^n1,2)", "templateType": "anything", "group": "Ungrouped variables", "name": "A1", "description": ""}, "P": {"definition": "random(2000..5000#100)", "templateType": "anything", "group": "Ungrouped variables", "name": "P", "description": ""}, "A2": {"definition": "precround(P*(1+int2)^n2,2)", "templateType": "anything", "group": "Ungrouped variables", "name": "A2", "description": ""}, "int1": {"definition": "perc1/100", "templateType": "anything", "group": "Ungrouped variables", "name": "int1", "description": ""}, "int3": {"definition": "perc2/365", "templateType": "anything", "group": "Ungrouped variables", "name": "int3", "description": ""}, "int2": {"definition": "perc2/36500", "templateType": "anything", "group": "Ungrouped variables", "name": "int2", "description": ""}, "perc1": {"definition": "random(5.2..6#0.1)", "templateType": "anything", "group": "Ungrouped variables", "name": "perc1", "description": ""}, "n1": {"definition": "random(2..4#1)", "templateType": "anything", "group": "Ungrouped variables", "name": "n1", "description": ""}, "n2": {"definition": "n1*365", "templateType": "anything", "group": "Ungrouped variables", "name": "n2", "description": ""}, "perc2": {"definition": "random(5.0..5.8#0.1)", "templateType": "anything", "group": "Ungrouped variables", "name": "perc2", "description": ""}}, "metadata": {"description": "<p>Compare two savings accounts with different interest rates.</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}]}]}], "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}]}