// Numbas version: finer_feedback_settings
{"name": "Annual Effective Rates", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["p", "a"], "name": "Annual Effective Rates", "tags": [], "advice": "<p>The nominal interest rate, $i^{(p)}$, is the nominal rate per annum payable p times a year over p periods. A capital amount $C$ accumulates to $C(1+i_{[p]})^p$ where $i_{[p]}={i^{(p)} \\over p}$</p>\n<p>Comparing this with $C(1+i)$ gives:</p>\n<p style=\"text-align: center;\">$1+i=(1+{i^{(p)} \\over p})^p$</p>\n<p style=\"text-align: left;\">where:</p>\n<ul>\n<li>$i$= annual effective rate</li>\n<li>$i^{(p)}$= nominal rate</li>\n<li>$p$= number of periods in a year</li>\n</ul>\n<p>Re-arranging this equation to make $i$ the subject of the formula gives:</p>\n<p style=\"text-align: center;\"><span>$i=(1+{i^{(p)} \\over p})^p-1$</span></p>\n<p style=\"text-align: left;\">In the above question:</p>\n<ul>\n<li>$i^{(p)}$={a}%</li>\n<li>$p$={p}</li>\n</ul>\n<p>Substituting these values in the above equation gives the annual effective rate $i$.</p>", "rulesets": {}, "parts": [{"precisionType": "dp", "precisionMessage": "<ul>\n<li>You have not given your answer to&nbsp;2 decimal places</li>\n<li>Your answer is wrong</li>\n</ul>", "allowFractions": false, "scripts": {}, "precision": "2", "maxValue": "(((1+({a}/{p*100}))^{p})-1)*100", "minValue": "(((1+({a}/{p*100}))^{p})-1)*100", "strictPrecision": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "marks": "2", "type": "numberentry", "showPrecisionHint": false}], "statement": "<p>What is the annual effective rate (% to two decimal places) if $i^{\\var{p}}$={a}%?</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"a": {"definition": "random(1..10#0.5)", "templateType": "randrange", "group": "Ungrouped variables", "name": "a", "description": ""}, "p": {"definition": "random([0.5,1,2,3,4,6,12,52,365])", "templateType": "anything", "group": "Ungrouped variables", "name": "p", "description": ""}}, "metadata": {"notes": "", "description": "", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Habiba Gora", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/494/"}]}]}], "contributors": [{"name": "Habiba Gora", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/494/"}]}