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The monthly interest rate is $\\var{perc}$% per month. There are 12 months in one year so the APR can be calculated as follows:

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$i=(1+\\frac{\\var{perc}}{100})^{12}-1=\\var{apr2}-1=\\var{apr}$

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Therefore the APR is $\\var{perc2}$%

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", "parts": [{"correctAnswerFraction": false, "minValue": "perc2-0.01", "variableReplacements": [], "showCorrectAnswer": true, "prompt": "

Calculate the Annual Percentage Rate (APR) for this credit card.

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Please give your answer as a percentage to two decimal places.

", "type": "numberentry", "maxValue": "perc2+0.01", "allowFractions": false, "marks": "5", "variableReplacementStrategy": "originalfirst", "scripts": {}, "showPrecisionHint": false}], "variable_groups": [], "ungrouped_variables": ["perc", "apr2", "int", "perc2", "apr"], "rulesets": {}, "name": "APR", "extensions": [], "tags": ["Annual Percentage Rate", "APR", "REBEL", "rebel", "Rebel", "rebelmaths"], "type": "question", "functions": {}, "preamble": {"css": "", "js": ""}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "questions": [], "pickQuestions": 0}], "variablesTest": {"condition": "", "maxRuns": 100}, "metadata": {"description": "

A credit card company charges compound interest at x% per month 
on unpaid balances.

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rebelmaths

", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "

A credit card company charges compound interest at a rate of $\\var{perc}$% per month on unpaid balances.

", "variables": {"perc": {"templateType": "anything", "definition": "random(0.8..1.6#0.1)", "description": "", "group": "Ungrouped variables", "name": "perc"}, "int": {"templateType": "anything", "definition": "perc/100", "description": "", "group": "Ungrouped variables", "name": "int"}, "perc2": {"templateType": "anything", "definition": "precround(apr*100,2)", "description": "", "group": "Ungrouped variables", "name": "perc2"}, "apr2": {"templateType": "anything", "definition": "precround((1+int)^12,4)", "description": "", "group": "Ungrouped variables", "name": "apr2"}, "apr": {"templateType": "anything", "definition": "precround(apr2-1,4)", "description": "", "group": "Ungrouped variables", "name": "apr"}}, "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/"}]}