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{"name": "the real rate of interest", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"ungrouped_variables": ["p", "pdec", "nomipa", "nomipadec", "realipadec", "realipa", "roundedrealipa"], "preamble": {"css": "", "js": ""}, "variablesTest": {"maxRuns": 100, "condition": ""}, "parts": [{"variableReplacements": [], "marks": 0, "prompt": "<p>If inflation was $\\var{p}\\%$ p.a. and the nominal interest rate was $\\var{nomipa}\\%$ p.a. then what would&nbsp;the real rate of interest be?</p>\n<p></p>\n<p>[[0]]$\\%$ p.a. (to 2 decimal places)</p>", "useCustomName": false, "gaps": [{"variableReplacements": [], "allowFractions": false, "marks": 1, "notationStyles": ["plain", "en", "si-en"], "minValue": "realipa", "useCustomName": false, "showCorrectAnswer": true, "precisionMessage": "You have not given your answer to the correct precision.", "unitTests": [], "precisionType": "dp", "correctAnswerFraction": false, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "mustBeReduced": false, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "scripts": {}, "maxValue": "realipa", "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "showPrecisionHint": false, "showFeedbackIcon": true, "precisionPartialCredit": 0, "customName": "", "strictPrecision": true, "precision": "2"}], "showFeedbackIcon": true, "showCorrectAnswer": true, "unitTests": [], "customName": "", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "type": "gapfill", "variableReplacementStrategy": "originalfirst", "scripts": {}, "sortAnswers": false}], "variable_groups": [], "extensions": [], "advice": "<p>We are asked to find the real rate of interest. Therefore we&nbsp;would use the equation</p>\n<p>$\\displaystyle i^*=\\left(\\frac{1+i}{1+p}\\right)-1$</p>\n<p>where $i^*$ is the real rate of interest, $i$ is the nominal rate of interest, and $p$ is the rate of inflation.</p>\n<p></p>\n<p>In our&nbsp;situation we have,&nbsp;</p>\n<p>$i=\\var{nomipa}\\%=\\var{nomipadec}$</p>\n<p>$p=\\var{p}\\%=\\var{pdec}$</p>\n<p>and therefore we have</p>\n<p>$\\begin{align} i^*&amp;=\\left(\\frac{1+\\var{nomipadec}}{1+\\var{pdec}}\\right)-1\\\\&amp;=\\frac{\\var{1+nomipadec}}{\\var{1+pdec}}-1\\\\&amp;\\approx \\var{realipadec}\\\\&amp;=\\var{roundedrealipa}\\%\\quad\\text{(to 2 decimal places)}\\end{align}$</p>", "name": "the real rate of interest", "variables": {"realipadec": {"templateType": "anything", "definition": "((1+nomipadec)/(1+pdec))-1", "description": "", "name": "realipadec", "group": "Ungrouped variables"}, "nomipadec": {"templateType": "anything", "definition": "nomipa/100", "description": "", "name": "nomipadec", "group": "Ungrouped variables"}, "p": {"templateType": "anything", "definition": "random(0.1..5#0.1)", "description": "<p>inflation</p>", "name": "p", "group": "Ungrouped variables"}, "nomipa": {"templateType": "anything", "definition": "p+random(1.5..8#0.1)", "description": "", "name": "nomipa", "group": "Ungrouped variables"}, "pdec": {"templateType": "anything", "definition": "p/100", "description": "", "name": "pdec", "group": "Ungrouped variables"}, "roundedrealipa": {"templateType": "anything", "definition": "precround(realipa,2)", "description": "", "name": "roundedrealipa", "group": "Ungrouped variables"}, "realipa": {"templateType": "anything", "definition": "realipadec*100", "description": "", "name": "realipa", "group": "Ungrouped variables"}}, "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>", "metadata": {"description": "Financial maths. Given the nominal interest rate and the rate of inflation determine the real rate of interest", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "functions": {}, "rulesets": {}, "tags": [], "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/"}]}