// Numbas version: exam_results_page_options
{"name": "Compound Interest - find interest rate", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"preamble": {"css": "", "js": ""}, "variables": {"n": {"definition": "random(4..10#1)", "name": "n", "group": "Ungrouped variables", "templateType": "randrange", "description": ""}, "A": {"definition": "random(115000..125000#100)", "name": "A", "group": "Ungrouped variables", "templateType": "randrange", "description": ""}, "int": {"definition": "a_p_rt-1", "name": "int", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "a_p_rt": {"definition": "(A/A0)^(1/n)", "name": "a_p_rt", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "A0": {"definition": "random(100000..111000#100)", "name": "A0", "group": "Ungrouped variables", "templateType": "randrange", "description": ""}, "a_p": {"definition": "A/A0", "name": "a_p", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "ip": {"definition": "int*100\n", "name": "ip", "group": "Ungrouped variables", "templateType": "anything", "description": ""}}, "advice": "<p>We use the Compound Interest Formula $A=P(1+i)^n$ where</p>\n<p>$A=\\var{A}$</p>\n<p>$P=\\var{A0}$</p>\n<p>$i=?$</p>\n<p>$n=\\var{n}$</p>\n<p>So, we get</p>\n<p>&nbsp;$\\var{A}=\\var{A0}(1+i)^\\var{n}$&nbsp;</p>\n<p>Divide both sides by $\\var{A0}$</p>\n<p>&nbsp;$\\frac{\\var{A}}{\\var{A0}}=(1+i)^\\var{n}$&nbsp;</p>\n<p>$\\var{a_p}=(1+i)^\\var{n}$&nbsp;</p>\n<p>Next,</p>\n<p>$\\var{a_p}^{\\frac{1}{\\var{n}}}=1+i$</p>\n<p>$\\var{a_p_rt}=1+i$</p>\n<p>So, $\\var{a_p_rt}-1=\\var{int}=i$</p>\n<p>And so the answer as a percentage is $\\var{ip}$%.</p>\n<p>Then, just round to the correct number of decimal places.</p>\n<p></p>", "variable_groups": [], "rulesets": {}, "extensions": [], "parts": [{"prompt": "<p>Calculate the annual interest rate.</p>\n<p><span>Please give your answer as a percentage to 3 decimal places.</span></p>\n<p>[[0]]%</p>", "variableReplacements": [], "scripts": {}, "marks": 0, "showCorrectAnswer": true, "gaps": [{"maxValue": "100*(({A}/{A0})^(1/{n}) - 1)", "precision": "3", "precisionType": "dp", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "variableReplacementStrategy": "originalfirst", "marks": "5", "variableReplacements": [], "scripts": {}, "correctAnswerFraction": false, "type": "numberentry", "allowFractions": false, "showCorrectAnswer": true, "minValue": "100*(({A}/{A0})^(1/{n}) - 1)", "showPrecisionHint": false, "strictPrecision": false}], "type": "gapfill", "variableReplacementStrategy": "originalfirst"}], "tags": ["rebel", "Rebel", "REBEL", "rebelmaths"], "statement": "<p>An investor puts &euro;$\\var{A0}$ in a banks saving account with a fixed interest rate earning compound interest. In return they receive &euro;$\\var{A}$ in $\\var{n}$ years time.&nbsp;</p>", "variablesTest": {"condition": "", "maxRuns": 100}, "showQuestionGroupNames": false, "type": "question", "name": "Compound Interest - find interest rate", "ungrouped_variables": ["A", "A0", "n", "a_p", "a_p_rt", "int", "ip"], "question_groups": [{"pickQuestions": 0, "name": "", "questions": [], "pickingStrategy": "all-ordered"}], "functions": {}, "metadata": {"description": "<p>Find i using compound interest formula A=P(1+i)^n</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}, {"name": "heike hoffmann", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2960/"}]}]}], "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}, {"name": "heike hoffmann", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2960/"}]}