// Numbas version: exam_results_page_options
{"name": "Interest rate - simple interest", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"parts": [{"showFeedbackIcon": true, "gaps": [{"showFeedbackIcon": true, "marks": 1, "customMarkingAlgorithm": "", "allowFractions": false, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "minValue": "ipa", "variableReplacements": [], "useCustomName": false, "maxValue": "ipa", "precision": "2", "correctAnswerFraction": false, "precisionPartialCredit": 0, "strictPrecision": false, "correctAnswerStyle": "plain", "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "precisionType": "dp", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showPrecisionHint": false, "customName": "", "mustBeReducedPC": 0, "precisionMessage": "You have not given your answer to&nbsp;2 decimal places.", "scripts": {}}], "marks": 0, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "useCustomName": false, "prompt": "<p>You&nbsp;deposit $\\$\\var{P}$ into&nbsp;a bank account. After $\\var{n}$ {period[0]}&nbsp;you have saved up $\\$\\var{S}$. Calculate the rate of simple interest per annum that you have earnt on your deposit.</p>\n<p></p>\n<p>[[0]]&nbsp;$\\%$ (to 2 decimal places)</p>", "unitTests": [], "customName": "", "type": "gapfill", "scripts": {}, "sortAnswers": false}], "tags": [], "metadata": {"licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "description": "Using simple interest determine the interest rate"}, "rulesets": {}, "functions": {}, "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"period": {"description": "", "templateType": "anything", "name": "period", "group": "Ungrouped variables", "definition": "random(['quarters', 4],['months',12],['days', 365])"}, "ipadec": {"description": "", "templateType": "anything", "name": "ipadec", "group": "Ungrouped variables", "definition": "int/(P*n/period[1])"}, "n": {"description": "", "templateType": "anything", "name": "n", "group": "Ungrouped variables", "definition": "random(5..40)"}, "int": {"description": "", "templateType": "anything", "name": "int", "group": "Ungrouped variables", "definition": "precround(P*n/period[1]*random(0.03..0.10#0.0001),2)"}, "S": {"description": "", "templateType": "anything", "name": "S", "group": "Ungrouped variables", "definition": "P+int"}, "iparounded": {"description": "<p>interest per annum as a percentage (add the symbol afterwards)</p>", "templateType": "anything", "name": "iparounded", "group": "Ungrouped variables", "definition": "precround(ipadec*100,2)"}, "P": {"description": "<p>present value</p>", "templateType": "anything", "name": "P", "group": "Ungrouped variables", "definition": "random(1000..100000#1000)"}, "ipa": {"description": "", "templateType": "anything", "name": "ipa", "group": "Ungrouped variables", "definition": "ipadec*100"}}, "preamble": {"css": "", "js": ""}, "extensions": [], "advice": "<p>We are asked to find the&nbsp;interest&nbsp;rate using simple&nbsp;interest. Therefore we could use the equation</p>\n<p>$I=Ptr$,</p>\n<p>where $I$ is the interest amount, $P$ is the present value, $r$ is the interest rate per annum&nbsp;and $t$ is the time in years.</p>\n<p>Note, $I$, the interest amount, will be the difference between the future value and the present value.&nbsp;</p>\n<p></p>\n<p>In our&nbsp;situation we have,</p>\n<p>$I=\\var{S}-\\var{P}=\\var{int}$,</p>\n<p>$P=\\var{P}$,</p>\n<p>$t=\\frac{\\var{n}}{\\var{period[1]}}$,&nbsp;</p>\n<p>and therefore we have</p>\n<p>$\\displaystyle \\var{int}=\\var{P}\\times \\frac{\\var{n}}{\\var{period[1]}}\\times r$</p>\n<p>which we need to rearrange to solve for $r$.</p>\n<p></p>\n<p>We want to get $r$ by itself. We can do this by dividing both sides by $\\var{P}\\times \\frac{\\var{n}}{\\var{period[1]}}$ (in order to remove the multiplication by $\\var{P}\\times \\frac{\\var{n}}{\\var{period[1]}}$)</p>\n<p>$\\displaystyle \\frac{\\var{int}}{\\var{P}\\times \\frac{\\var{n}}{\\var{period[1]}}}=r$</p>\n<p>Calculating this we find&nbsp;</p>\n<p>$\\begin{align}r&amp;\\approx\\var{ipadec}\\\\&amp;=\\var{iparounded}\\%\\text{ &nbsp; &nbsp; &nbsp; &nbsp;(to 2 decimal places)}\\end{align}$</p>", "ungrouped_variables": ["P", "int", "S", "period", "n", "ipadec", "ipa", "iparounded"], "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>", "variable_groups": [], "name": "Interest rate - simple interest", "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/"}]}