// Numbas version: exam_results_page_options
{"name": "Simple and Compound Interest", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["capital", "interest", "z", "n", "ci", "si"], "name": "Simple and Compound Interest", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "<ul>\n<li><strong>Simple Interest</strong></li>\n</ul>\n<p>The general formula for the total amount after interest is earned is given by:</p>\n<p style=\"text-align: center;\">$C(1+ni)=Z$</p>\n<p style=\"text-align: left;\">where:</p>\n<ul>\n<li>$C$=capital</li>\n<li>$n$=period of time</li>\n<li>$i$=interest rate</li>\n<li>$Z$=capital+interest earned</li>\n</ul>\n<p>Re-arranging this formula to make $i$ the subject of the formula, you get:</p>\n<p style=\"text-align: center;\">$i={({1 \\over n})}{({Z \\over C}}-1)={Z-C&nbsp;\\over&nbsp;nC}$<br/><br/></p>\n<p style=\"text-align: left;\">In this question:</p>\n<ul>\n<li>$C$={capital}</li>\n<li>$n$={n}</li>\n<li>$Z$={capital}+{interest}={z}</li>\n</ul>\n<ul>\n<li><strong>Compound Interest</strong></li>\n</ul>\n<p>An capital $C$ lent over a period of $n$ years at an interest rate $i$ grows to</p>\n<p style=\"text-align: center;\">$C(1+i)^n=Z$</p>\n<p style=\"text-align: left;\"><span style=\"text-align: right;\">where $Z$ is the capital +interest earned.</span></p>\n<p style=\"text-align: left;\"><span style=\"text-align: right;\">Re-arranging this formula to make $i$ the subject of the formula gives:</span></p>\n<p style=\"text-align: left;\"><span style=\"text-align: right;\"> </span></p>\n<p style=\"text-align: left;\"><span style=\"text-align: right;\"> </span></p>\n<p style=\"text-align: center;\"><span>$i=({Z \\over C})^{1 \\over n}-1$</span></p>\n<p style=\"text-align: left;\"><span>In this question:</span></p>\n<ul>\n<li>$C$={capital}</li>\n<li>$n$={n}</li>\n<li>$Z$={capital}+{interest}={z}</li>\n</ul>\n<p></p>\n<p>Substituting these value into the above equations will give the simple and compound interest rates.</p>\n<p></p>\n<p></p>", "rulesets": {}, "parts": [{"precisionType": "dp", "prompt": "<p>simple interest is used?</p>", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{si}", "strictPrecision": true, "minValue": "{si}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": "50", "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "prompt": "<p>compound interest is used?</p>", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ci}", "strictPrecision": true, "minValue": "{ci}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": "50", "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": "2", "type": "numberentry", "showPrecisionHint": false}], "extensions": [], "statement": "<p>What is the interest rate (% to two decimal places) if the capital is <strong>&pound;{capital}</strong> and the interest earned is <strong>&pound;{interest}</strong> over a period of <strong>{n}</strong> years if:</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"ci": {"definition": "(((({interest}+{capital})/{capital})^(1/n))-1)*100", "templateType": "anything", "group": "Ungrouped variables", "name": "ci", "description": ""}, "n": {"definition": "random(2..10#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "n", "description": ""}, "si": {"definition": "(((({interest}+{capital})/{capital})-1)/n)*100", "templateType": "anything", "group": "Ungrouped variables", "name": "si", "description": ""}, "interest": {"definition": "random(50..200#15)", "templateType": "randrange", "group": "Ungrouped variables", "name": "interest", "description": ""}, "capital": {"definition": "random(100..800#50)", "templateType": "randrange", "group": "Ungrouped variables", "name": "capital", "description": ""}, "z": {"definition": "{capital}+{interest}", "templateType": "anything", "group": "Ungrouped variables", "name": "z", "description": ""}}, "metadata": {"description": "<p>Checking your knowledge of simple and compound interest</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Rachel Staddon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/901/"}]}]}], "contributors": [{"name": "Rachel Staddon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/901/"}]}