// Numbas version: exam_results_page_options {"name": "the effective rate of interest (given per period)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"parts": [{"showFeedbackIcon": true, "gaps": [{"showFeedbackIcon": true, "marks": 1, "customMarkingAlgorithm": "", "allowFractions": false, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "minValue": "ei", "variableReplacements": [], "useCustomName": false, "maxValue": "ei", "precision": "2", "correctAnswerFraction": false, "precisionPartialCredit": 0, "strictPrecision": true, "correctAnswerStyle": "plain", "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "precisionType": "dp", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showPrecisionHint": false, "customName": "", "mustBeReducedPC": 0, "precisionMessage": "You have not given your answer to 2 decimal places.", "scripts": {}}], "marks": 0, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "useCustomName": false, "prompt": "
Calculate the effective annual rate of interest that corresponds to $\\var{int}\\%$ per {period[0]}.
\n\n[[0]] $\\%$ p.a. (to 2 decimal places)
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\n$\\displaystyle i_e=\\left(1+\\frac{j}{m}\\right)^m-1$,
\nwhere $i_e$ is the effective interest rate, $j$ is the nominal interest rate, $m$ the number of compounding periods per year.
\nIn our situation we have,
\n$j=\\var{int}\\%\\times \\var{period[1]}=\\var{nom}\\%=\\var{nomdec}$
\n$m=\\var{period[1]}$
\nand therefore we have
\n$\\begin{align} i_e&=\\left(1+\\frac{\\var{nomdec}}{\\var{period[1]}}\\right)^\\var{period[1]}-1\\\\&\\approx \\var{eidec}\\\\&=\\var{eirounded}\\%\\quad \\text{(to 2 decimal places)}\\end{align}$
", "ungrouped_variables": ["seed", "int", "period", "nom", "nomdec", "eidec", "ei", "eirounded"], "statement": "If you are unsure of how to do a question, click on Reveal answers to see the full working. Then, once you understand how to do the question, click on Try another question like this one to start again. Do each question repeatedly to ensure you have mastered it.
", "variable_groups": [], "name": "the effective rate of interest (given per period)", "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}