// Numbas version: exam_results_page_options
{"name": "the effective rate of interest (given nominal)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variablesTest": {"maxRuns": 100, "condition": ""}, "statement": "<p>If you are unsure of how to do&nbsp;a question, click on&nbsp;<em>Reveal answers</em>&nbsp;to see the full working. Then, once you understand how to do the question, click on&nbsp;<em>Try another question like this one</em>&nbsp;to start again. Do each question repeatedly to ensure you have mastered it.</p>", "name": "the effective rate of interest (given nominal)", "rulesets": {}, "tags": [], "preamble": {"js": "", "css": ""}, "functions": {}, "parts": [{"scripts": {}, "unitTests": [], "type": "gapfill", "gaps": [{"unitTests": [], "mustBeReducedPC": 0, "precisionPartialCredit": 0, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "precisionType": "dp", "allowFractions": false, "mustBeReduced": false, "maxValue": "ei", "marks": 1, "scripts": {}, "type": "numberentry", "precisionMessage": "You have not given your answer to&nbsp;2 decimal places.", "useCustomName": false, "precision": "2", "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "minValue": "ei", "showCorrectAnswer": true, "correctAnswerFraction": false, "customName": "", "extendBaseMarkingAlgorithm": true, "strictPrecision": true, "showFeedbackIcon": true, "correctAnswerStyle": "plain", "showPrecisionHint": false}], "useCustomName": false, "prompt": "<p>Calculate the effective annual rate of interest&nbsp;that corresponds to $\\var{nom}\\%$ per annum compounded {period[0]}.&nbsp;</p>\n<p></p>\n<p>[[0]] $\\%$ p.a. (to 2 decimal places)</p>", "sortAnswers": false, "variableReplacements": [], "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "customName": "", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "marks": 0}], "advice": "<p>We are asked to find the effective&nbsp;rate of interest. Therefore we will use the following&nbsp;formula</p>\n<p>$\\displaystyle i_e=\\left(1+\\frac{j}{m}\\right)^m-1$,</p>\n<p>where $i_e$ is the effective interest rate, $j$ is the nominal interest rate, $m$ the number of compounding periods per year.</p>\n<p>In our&nbsp;situation we have,&nbsp;</p>\n<p>$j=\\var{nom}\\%=\\var{nomdec}$</p>\n<p>$m=\\var{period[1]}$&nbsp;</p>\n<p>and therefore we have</p>\n<p>$\\begin{align} i_e&amp;=\\left(1+\\frac{\\var{nomdec}}{\\var{period[1]}}\\right)^\\var{period[1]}-1\\\\&amp;\\approx \\var{eidec}\\\\&amp;=\\var{eirounded}\\%\\quad \\text{(to 2 decimal places)}\\end{align}$</p>", "extensions": [], "metadata": {"description": "Financial maths question.&nbsp;", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "variables": {"eirounded": {"definition": "precround(ei,2)", "description": "", "group": "Ungrouped variables", "name": "eirounded", "templateType": "anything"}, "nomdec": {"definition": "nom/100", "description": "", "group": "Ungrouped variables", "name": "nomdec", "templateType": "anything"}, "nom": {"definition": "int*period[1]", "description": "", "group": "Ungrouped variables", "name": "nom", "templateType": "anything"}, "ei": {"definition": "eidec*100", "description": "", "group": "Ungrouped variables", "name": "ei", "templateType": "anything"}, "eidec": {"definition": "((1+int/100)^period[1])-1", "description": "", "group": "Ungrouped variables", "name": "eidec", "templateType": "anything"}, "period": {"definition": "random([random('half-yearly', 'semi-annually'),2],['quarterly', 4],['monthly',12],['daily', 365])", "description": "", "group": "Ungrouped variables", "name": "period", "templateType": "anything"}, "seed": {"definition": "random(0.02..0.12#0.001)", "description": "", "group": "Ungrouped variables", "name": "seed", "templateType": "anything"}, "int": {"definition": "precround((seed/period[1])*100,2)", "description": "", "group": "Ungrouped variables", "name": "int", "templateType": "anything"}}, "variable_groups": [], "ungrouped_variables": ["seed", "int", "period", "nom", "nomdec", "eidec", "ei", "eirounded"], "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/"}]}