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{"name": "number of time periods - simple interest", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"metadata": {"description": "Using simple interest determine the number of days needed", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "advice": "<p>We are asked to find the number of time periods using simple interest. Therefore we could use the equation</p>\n<p>$S=P(1+rt)$,</p>\n<p>where $S$ is the future value, $P$ is the present value, $r$ is the interest rate per annum&nbsp;and $t$ is the time in years.</p>\n<p></p>\n<p>In our&nbsp;situation we have,</p>\n<p>$S=\\var{S}$,</p>\n<p>$P=\\var{P}$,</p>\n<p>$r=\\var{ipa}\\%=\\var{ipadec}$,&nbsp;</p>\n<p>and therefore we have</p>\n<p>$ \\var{S}=\\var{P}(1+\\var{ipadec}t)$</p>\n<p>which we need to rearrange to solve for $t$.</p>\n<p></p>\n<p>We want to get $t$ by itself. We&nbsp;start by&nbsp;dividing both sides by $\\var{P}$ (in order to remove the multiplication by $\\var{P}$)</p>\n<p>$\\displaystyle \\frac{\\var{S}}{\\var{P}}=1+\\var{ipadec}t$</p>\n<p>Next we will subtract $1$ from both sides&nbsp;</p>\n<p>$\\displaystyle \\frac{\\var{S}}{\\var{P}}-1=\\var{ipadec}t$</p>\n<p>Then we will divide both sides by $\\var{ipadec}$ (in order to remove the multiplication by $\\var{ipadec}$)</p>\n<p>$\\displaystyle \\frac{\\frac{\\var{S}}{\\var{P}}-1}{\\var{ipadec}}=t$</p>\n<p></p>\n<p></p>\n<p>Calculating this we find&nbsp;</p>\n<p>$t\\approx\\var{years}\\quad \\text{years}$.</p>\n<p>Since we are asked for the number of days we multiply by $365$</p>\n<p>$\\text{number of days}\\approx \\var{days}$</p>\n<p>but we don't round this in the traditional sense since we require an entire time period to elapse for the interest to be paid, therefore we always round&nbsp;<em>up</em>&nbsp;to the nearest whole number.</p>\n<p>That is, we need to wait $\\var{daysrounded}$&nbsp;days.</p>", "extensions": [], "preamble": {"js": "", "css": ""}, "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>", "variables": {"days": {"definition": "years*365", "name": "days", "templateType": "anything", "description": "", "group": "Ungrouped variables"}, "daysrounded": {"definition": "ceil(days)", "name": "daysrounded", "templateType": "anything", "description": "", "group": "Ungrouped variables"}, "period": {"definition": "['days', 365]", "name": "period", "templateType": "anything", "description": "", "group": "Ungrouped variables"}, "ipa": {"definition": "ipadec*100", "name": "ipa", "templateType": "anything", "description": "", "group": "Ungrouped variables"}, "P": {"definition": "random(1000..100000#1000)", "name": "P", "templateType": "anything", "description": "<p>present value</p>", "group": "Ungrouped variables"}, "years": {"definition": "(S/P-1)/ipadec", "name": "years", "templateType": "anything", "description": "", "group": "Ungrouped variables"}, "ipadec": {"definition": "random(0.04..0.10#0.001)", "name": "ipadec", "templateType": "anything", "description": "", "group": "Ungrouped variables"}, "S": {"definition": "precround(P*(1+(ipadec+random(-0.03..0.03))*random(30..365)/365),0)", "name": "S", "templateType": "anything", "description": "", "group": "Ungrouped variables"}}, "functions": {}, "name": "number of time periods - simple interest", "tags": [], "rulesets": {}, "ungrouped_variables": ["P", "S", "ipadec", "ipa", "period", "years", "days", "daysrounded"], "parts": [{"sortAnswers": false, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "customName": "", "unitTests": [], "prompt": "<p>You&nbsp;deposit&nbsp;$\\$\\var{P}$ into a bank account with a simple interest rate of $\\var{ipa}\\%$ per annum.&nbsp;How many&nbsp;days will it take&nbsp;for the balance to be at least $\\$\\var{S}$?&nbsp;</p>\n<p></p>\n<p>[[0]]&nbsp;&nbsp;days</p>", "type": "gapfill", "scripts": {}, "customMarkingAlgorithm": "", "gaps": [{"variableReplacements": [], "extendBaseMarkingAlgorithm": true, "minValue": "daysrounded", "customName": "", "unitTests": [], "correctAnswerStyle": "plain", "type": "numberentry", "correctAnswerFraction": false, "scripts": {}, "customMarkingAlgorithm": "", "maxValue": "daysrounded", "mustBeReduced": false, "mustBeReducedPC": 0, "showFeedbackIcon": true, "showFractionHint": true, "useCustomName": false, "variableReplacementStrategy": "originalfirst", "marks": 1, "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "allowFractions": false}], "showFeedbackIcon": true, "useCustomName": false, "variableReplacementStrategy": "originalfirst", "marks": 0, "showCorrectAnswer": true}], "variablesTest": {"condition": "", "maxRuns": 100}, "variable_groups": [], "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/"}]}