// Numbas version: finer_feedback_settings
{"name": "Simon's copy of Savings compound interest 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"parts": [{"showFeedbackIcon": true, "variableReplacements": [], "gaps": [{"showFeedbackIcon": true, "minValue": "P", "variableReplacements": [], "customMarkingAlgorithm": "", "correctAnswerStyle": "plain", "extendBaseMarkingAlgorithm": true, "customName": "", "correctAnswerFraction": false, "mustBeReducedPC": 0, "showCorrectAnswer": true, "maxValue": "P", "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "scripts": {}, "showFractionHint": true, "variableReplacementStrategy": "originalfirst", "unitTests": [], "mustBeReduced": false, "useCustomName": false, "marks": 1, "type": "numberentry"}], "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "customName": "", "sortAnswers": false, "showCorrectAnswer": true, "scripts": {}, "prompt": "<p>What is the value of $P$?</p>\n<p><span>&pound;[[0]]</span></p>", "variableReplacementStrategy": "originalfirst", "unitTests": [], "useCustomName": false, "marks": 0, "type": "gapfill"}, {"showFeedbackIcon": true, "variableReplacements": [], "gaps": [{"showFeedbackIcon": true, "minValue": "int", "variableReplacements": [], "customMarkingAlgorithm": "", "correctAnswerStyle": "plain", "extendBaseMarkingAlgorithm": true, "customName": "", "correctAnswerFraction": false, "mustBeReducedPC": 0, "showCorrectAnswer": true, "maxValue": "int", "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "scripts": {}, "showFractionHint": true, "variableReplacementStrategy": "originalfirst", "unitTests": [], "mustBeReduced": false, "useCustomName": false, "marks": 1, "type": "numberentry"}], "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "customName": "", "sortAnswers": false, "showCorrectAnswer": true, "scripts": {}, "prompt": "<p>What is the value of $r$?</p>\n<p><span>[[0]]</span></p>", "variableReplacementStrategy": "originalfirst", "unitTests": [], "useCustomName": false, "marks": 0, "type": "gapfill"}, {"showFeedbackIcon": true, "variableReplacements": [], "gaps": [{"showFeedbackIcon": true, "minValue": "n", "variableReplacements": [], "customMarkingAlgorithm": "", "correctAnswerStyle": "plain", "extendBaseMarkingAlgorithm": true, "customName": "", "correctAnswerFraction": false, "mustBeReducedPC": 0, "showCorrectAnswer": true, "maxValue": "n", "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "scripts": {}, "showFractionHint": true, "variableReplacementStrategy": "originalfirst", "unitTests": [], "mustBeReduced": false, "useCustomName": false, "marks": 1, "type": "numberentry"}], "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "customName": "", "sortAnswers": false, "showCorrectAnswer": true, "scripts": {}, "prompt": "<p>What is the value of $n$?</p>\n<p><span></span></p>\n<p><span>[[0]]</span></p>", "variableReplacementStrategy": "originalfirst", "unitTests": [], "useCustomName": false, "marks": 0, "type": "gapfill"}, {"showFeedbackIcon": true, "variableReplacements": [], "gaps": [{"showFeedbackIcon": true, "minValue": "A", "variableReplacements": [], "customMarkingAlgorithm": "", "correctAnswerStyle": "plain", "extendBaseMarkingAlgorithm": true, "customName": "", "correctAnswerFraction": false, "mustBeReducedPC": 0, "showCorrectAnswer": true, "maxValue": "A", "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "scripts": {}, "showFractionHint": true, "variableReplacementStrategy": "originalfirst", "unitTests": [], "mustBeReduced": false, "useCustomName": false, "marks": "2", "type": "numberentry"}], "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "customName": "", "sortAnswers": false, "showCorrectAnswer": true, "scripts": {}, "prompt": "<p>How much will be in the&nbsp;deposit account after&nbsp;$\\var{n}$ years? Please give your answer to the nearest penny.</p>\n<p>&pound;[[0]]</p>", "variableReplacementStrategy": "originalfirst", "unitTests": [], "useCustomName": false, "marks": 0, "type": "gapfill"}, {"showFeedbackIcon": true, "variableReplacements": [], "gaps": [{"showFeedbackIcon": true, "precisionMessage": "You have not given your answer to the correct precision.", "customMarkingAlgorithm": "", "correctAnswerStyle": "plain", "strictPrecision": false, "correctAnswerFraction": false, "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "maxValue": "A-P", "allowFractions": false, "variableReplacementStrategy": "originalfirst", "unitTests": [], "precision": "2", "marks": 1, "minValue": "A-P", "variableReplacements": [], "precisionType": "dp", "extendBaseMarkingAlgorithm": true, "customName": "Total Interest", "scripts": {}, "type": "numberentry", "showPrecisionHint": false, "mustBeReduced": false, "useCustomName": true, "showCorrectAnswer": true, "precisionPartialCredit": 0}], "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "customName": "", "sortAnswers": false, "showCorrectAnswer": true, "scripts": {}, "prompt": "<p>How much interest was earned in total? Give your answer to the nearest penny.</p>\n<p>&pound;[[0]]</p>\n<p></p>", "variableReplacementStrategy": "originalfirst", "unitTests": [], "useCustomName": false, "marks": 0, "type": "gapfill"}], "functions": {}, "name": "Simon's copy of Savings compound interest 1", "tags": [], "extensions": [], "variablesTest": {"condition": "", "maxRuns": 100}, "variable_groups": [], "ungrouped_variables": ["n", "P", "A", "perc", "int", "ratio", "intplus"], "variables": {"A": {"definition": "precround(P*(1+int)^n,2)", "group": "Ungrouped variables", "description": "", "name": "A", "templateType": "anything"}, "intplus": {"definition": "ratio^(1/n)", "group": "Ungrouped variables", "description": "", "name": "intplus", "templateType": "anything"}, "P": {"definition": "random(1000..6000 #500)", "group": "Ungrouped variables", "description": "", "name": "P", "templateType": "anything"}, "int": {"definition": "perc/100", "group": "Ungrouped variables", "description": "", "name": "int", "templateType": "anything"}, "n": {"definition": "random(2..6 #1)", "group": "Ungrouped variables", "description": "", "name": "n", "templateType": "anything"}, "ratio": {"definition": "A/P", "group": "Ungrouped variables", "description": "", "name": "ratio", "templateType": "anything"}, "perc": {"definition": "random(1.5..5.5 #0.5)", "group": "Ungrouped variables", "description": "", "name": "perc", "templateType": "anything"}}, "rulesets": {}, "preamble": {"css": "", "js": ""}, "advice": "<p><span>The compound interest formula is: $\\ A = P(1+r)^n $</span></p>\n<p><strong></strong></p>\n<p><strong>(a)</strong></p>\n<p>$P$&nbsp;represents the principal sum invested, so in this example it is &euro;$\\var{P}$.</p>\n<p><strong></strong></p>\n<p><strong>(b)</strong></p>\n<p>$r$ represents the rate of compound interest, as a decimal. Since our interest rate is $\\var{100*int}$%, as a decimal this is<span>&nbsp;$\\frac{\\var{100*int}}{100}=\\var{int}$</span></p>\n<p><strong></strong></p>\n<p><strong>(c)</strong></p>\n<p>$n$&nbsp;represents the number of compounding periods, so in this example it is $\\var{n}$ years.</p>\n<p><strong></strong></p>\n<p><strong>(d)</strong></p>\n<p><span>Using the compound interest formula:</span></p>\n<p><span>$A=P(1+r)^n$</span></p>\n<p><span>$A=\\var{P}(1+\\var{int})^\\var{n} = \\var{P*(1+int)^n}=&pound;\\var{A}$ to the nearest penny.</span></p>\n<p><span></span></p>\n<p><strong>(e)</strong></p>\n<p>The total interest earnt is the difference between the final amount and the principal invested.&nbsp;</p>\n<p></p>\n<p>Interest = $A-P=\\var{A}-\\var{P}=&pound;\\var{dpformat(A-P,2)}$</p>\n<p><span></span></p>", "metadata": {"description": "<p><span style=\"color: rgb(34, 34, 34);\">Calculate the final amount in a savings account where compound interest is earned annually&nbsp;</span><br></p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>A lump sum of &pound;$\\var{P}$ is deposited into a savings account that pays compound interest for $\\var{n}$ years at a rate of $\\var{int*100}$% per annum. If no withdrawals are made from the account, then the amount that the lump sum will have grown to is given by the&nbsp;compound interest formula:</p>\n<p>$\\ A = P(1+r)^n $</p>", "type": "question", "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}]}], "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}