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{"name": "Consumer Arithmetic -  Simple Interest", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"preamble": {"js": "", "css": ""}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Calculate the interest accrued in a savings account, given the initial balance and annual interest rate.</p>"}, "rulesets": {}, "statement": "<p>Suppose you put \\${money} into a savings account&nbsp;exactly {years} years ago and you haven't touched the money since. The simple interest rate on the account is {perc2}% per year.</p>", "variables": {"years": {"group": "Ungrouped variables", "definition": "random(2..6)", "description": "", "templateType": "anything", "name": "years"}, "money": {"group": "Ungrouped variables", "definition": "random(100..5000 #100)", "description": "", "templateType": "anything", "name": "money"}, "perc2": {"group": "Ungrouped variables", "definition": "random(0..2.5 #0.05)", "description": "", "templateType": "anything", "name": "perc2"}}, "variablesTest": {"maxRuns": 100, "condition": ""}, "name": "Consumer Arithmetic -  Simple Interest", "functions": {}, "advice": "<p>This is <em>simple</em> interest, which means the amount added each year is a percentage of the <strong>original</strong> amount. The amount we add is fixed for all {years} years.</p>\n<p>First,&nbsp;we work out the amount of interest for one year:</p>\n<p>\\begin{align} <br/>\\var{perc2} \\text{% of } \\var{money} &amp;= \\frac{\\var{perc2}}{100} \\times \\var{money} \\\\<br/>&amp;= \\var{perc2/100} \\times \\var{money} \\\\<br/>&amp;= &pound;\\var{dpformat(perc2/100*money,2)} \\text{.}&nbsp;<br/>\\end{align}</p>\n<p>The money has been in the account for {years} years, so we multiply $&pound;\\var{dpformat(perc2/100*money,2)}$ by $\\var{years}$.</p>\n<p>\\[ &pound;\\var{dpformat(perc2/100*money,2)} \\times \\var{years} = &pound;\\var{dpformat(perc2/100*money*years,2)} \\text{.} \\]</p>\n<p>Adding this to the original balance:</p>\n<p>\\[ &pound;\\var{money} + &pound;\\var{dpformat(perc2/100*money*years,2)}&nbsp; = &pound;\\var{dpformat(perc2/100*money*years + money,2)} \\text{.} \\]</p>\n<p>This is the amount we would get if we withdrew the whole savings balance today.</p>", "parts": [{"type": "gapfill", "sortAnswers": false, "unitTests": [], "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "prompt": "<p>&nbsp;If you were to withdraw the money from this account now, how much&nbsp;would you have?</p>\n<p>$&nbsp;[[0]]</p>", "marks": 0, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "gaps": [{"type": "numberentry", "maxValue": "(1 + perc2/100*years)*money", "correctAnswerFraction": false, "mustBeReduced": false, "customMarkingAlgorithm": "", "variableReplacements": [], "showCorrectAnswer": false, "scripts": {}, "strictPrecision": true, "precisionPartialCredit": 0, "notationStyles": ["plain", "en", "si-en"], "precisionMessage": "You have not given your answer to the correct precision.", "unitTests": [], "mustBeReducedPC": 0, "variableReplacementStrategy": "originalfirst", "precision": "2", "correctAnswerStyle": "plain", "marks": "2", "extendBaseMarkingAlgorithm": true, "showPrecisionHint": true, "showFeedbackIcon": true, "allowFractions": false, "minValue": "(1 + perc2/100*years)*money", "precisionType": "dp"}], "scripts": {}, "showFeedbackIcon": true}], "extensions": [], "ungrouped_variables": ["perc2", "money", "years"], "tags": [], "variable_groups": [], "type": "question", "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Stanislav Duris", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1590/"}, {"name": "Paul Hancock", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1738/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Stanislav Duris", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1590/"}, {"name": "Paul Hancock", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1738/"}]}