// Numbas version: finer_feedback_settings
{"name": "Force of Interest", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["interest", "fi", "force", "int"], "name": "Force of Interest", "tags": [], "advice": "<p>The force of interest, $\\delta$, is defined as the nominal rate of interest payable continuously.</p>\n<p style=\"text-align: center;\">$lim_{p\\to\\infty} i^{(p)}=\\delta$</p>\n<p style=\"text-align: left;\">As the relationship between the effective and the nominal rate is given by (see&nbsp;<a href=\"/numbas-previews/question-8449-nominal-rates/index.html\">Numbas- Nominal Rates</a>):</p>\n<p style=\"text-align: center;\">$1+i=(1+{i^{(p)} \\over p})^p$</p>\n<p style=\"text-align: left;\">then in the limit as $p\\to\\infty$:</p>\n<p style=\"text-align: center;\">$1+i=lim_{p\\to\\infty}(1+{\\delta \\over p})^p=e^\\delta$</p>\n<p style=\"text-align: left;\"><span>so then:</span></p>\n<p style=\"text-align: center;\"><span>$ln(1+i)=\\delta$ and $i=e^\\delta-1$</span></p>\n<p>where:</p>\n<ul>\n<li>$i$= effective interest rate</li>\n<li>$ln$= natural logarithm</li>\n<li>$\\delta$= force of interest</li>\n</ul>\n<p>Substituting the values from the questions into these equations will give you the force of interest and the&nbsp;<span>effective interest rate.</span></p>", "rulesets": {}, "parts": [{"precisionType": "dp", "prompt": "<p>What is the force of interest (% to two decimal place) if the interest rate is {interest}%?</p>", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "scripts": {}, "precision": "2", "maxValue": "{fi}*100", "minValue": "{fi}*100", "strictPrecision": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "marks": "2", "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "prompt": "<p>What is the interest rate (% to two decimal places) if $\\delta$={force}%?</p>", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "scripts": {}, "precision": "2", "maxValue": "{int}*100", "minValue": "{int}*100", "strictPrecision": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "marks": "2", "type": "numberentry", "showPrecisionHint": false}], "statement": "", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"int": {"definition": "(e^({force}/100))-1", "templateType": "anything", "group": "Ungrouped variables", "name": "int", "description": ""}, "fi": {"definition": "ln(1+({interest}/100))", "templateType": "anything", "group": "Ungrouped variables", "name": "fi", "description": ""}, "force": {"definition": "random(1..10#0.5)", "templateType": "randrange", "group": "Ungrouped variables", "name": "force", "description": ""}, "interest": {"definition": "random(1..10#0.5)", "templateType": "randrange", "group": "Ungrouped variables", "name": "interest", "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/"}]}