// Numbas version: exam_results_page_options
{"name": "Simon's copy of 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": [{"metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Find i using compound interest formula A=P(1+i)^n</p>\n<p>rebelmaths</p>"}, "preamble": {"js": "", "css": ""}, "variables": {"int": {"templateType": "anything", "group": "Ungrouped variables", "definition": "a_p_rt-1", "name": "int", "description": ""}, "n": {"templateType": "randrange", "group": "Ungrouped variables", "definition": "random(4 .. 10#1)", "name": "n", "description": ""}, "ip": {"templateType": "anything", "group": "Ungrouped variables", "definition": "int*100\n", "name": "ip", "description": ""}, "A0": {"templateType": "randrange", "group": "Ungrouped variables", "definition": "random(100000 .. 111000#100)", "name": "A0", "description": ""}, "A": {"templateType": "randrange", "group": "Ungrouped variables", "definition": "random(115000 .. 125000#100)", "name": "A", "description": ""}, "a_p_rt": {"templateType": "anything", "group": "Ungrouped variables", "definition": "(A/A0)^(1/n)", "name": "a_p_rt", "description": ""}, "a_p": {"templateType": "anything", "group": "Ungrouped variables", "definition": "A/A0", "name": "a_p", "description": ""}}, "extensions": [], "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>", "rulesets": {}, "tags": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "ungrouped_variables": ["A", "A0", "n", "a_p", "a_p_rt", "int", "ip"], "variable_groups": [], "functions": {}, "parts": [{"variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "type": "gapfill", "useCustomName": false, "gaps": [{"precisionType": "dp", "extendBaseMarkingAlgorithm": true, "precision": "3", "useCustomName": false, "marks": "5", "minValue": "100*(({A}/{A0})^(1/{n}) - 1)", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "strictPrecision": false, "allowFractions": false, "mustBeReduced": false, "customName": "", "precisionMessage": "You have not given your answer to the correct precision.", "variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "maxValue": "100*(({A}/{A0})^(1/{n}) - 1)", "type": "numberentry", "mustBeReducedPC": 0, "showCorrectAnswer": true, "precisionPartialCredit": 0, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "scripts": {}, "unitTests": [], "showPrecisionHint": false, "variableReplacements": []}], "marks": 0, "sortAnswers": false, "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "customMarkingAlgorithm": "", "scripts": {}, "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>", "customName": "", "unitTests": []}], "name": "Simon's copy of Compound Interest - find interest rate", "advice": "<p>We use the Compound Interest Formula $A=P(1+r)^n$ where</p>\n<p>$A=\\var{A}$</p>\n<p>$P=\\var{A0}$</p>\n<p>$r=?$</p>\n<p>$n=\\var{n}$</p>\n<p>So, we get</p>\n<p>&nbsp;$\\var{A}=\\var{A0}(1+r)^\\var{n}$&nbsp;</p>\n<p>Divide both sides by $\\var{A0}$</p>\n<p>&nbsp;$\\frac{\\var{A}}{\\var{A0}}=(1+r)^\\var{n}$&nbsp;</p>\n<p>$\\var{a_p}=(1+r)^\\var{n}$&nbsp;</p>\n<p>Next,</p>\n<p>$\\var{a_p}^{\\frac{1}{\\var{n}}}=1+r$</p>\n<p>$\\var{a_p_rt}=1+r$</p>\n<p>So, $\\var{a_p_rt}-1=\\var{int}=r$</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>", "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/"}]}