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", "name": "Opportunity cost", "ungrouped_variables": ["et", "lt", "a", "OCdec", "OC", "OCrounded"], "rulesets": {}, "variable_groups": [], "tags": [], "metadata": {"licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "description": "Financial maths. Determine the cost of forgoing a discount."}, "variables": {"lt": {"name": "lt", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "3*et"}, "OCdec": {"name": "OCdec", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "a/(100-a)*365/(lt-et)"}, "et": {"name": "et", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(15,20,30)"}, "a": {"name": "a", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..6)"}, "OC": {"name": "OC", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "OCdec*100"}, "OCrounded": {"name": "OCrounded", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "precround(OC,2)"}}, "functions": {}, "parts": [{"sortAnswers": false, "prompt": "The annual cost of forgoing a cash discount under the terms of sale $\\var{a}/\\var{et}$ $n/\\var{lt}$ would be
\n[[0]] $\\%$ p.a. (to two decimal places)
", "customName": "", "showCorrectAnswer": true, "marks": 0, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "variableReplacements": [], "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "gaps": [{"correctAnswerFraction": false, "showFeedbackIcon": true, "precisionPartialCredit": 0, "mustBeReduced": false, "mustBeReducedPC": 0, "correctAnswerStyle": "plain", "customName": "", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "strictPrecision": false, "precisionType": "dp", "useCustomName": false, "allowFractions": false, "showCorrectAnswer": true, "marks": 1, "variableReplacementStrategy": "originalfirst", "precision": "2", "variableReplacements": [], "scripts": {}, "maxValue": "OCrounded", "minValue": "OCrounded", "type": "numberentry", "unitTests": [], "precisionMessage": "You have not given your answer to the correct precision."}], "type": "gapfill", "unitTests": [], "useCustomName": false}], "preamble": {"js": "", "css": ""}, "variablesTest": {"maxRuns": 100, "condition": "\n"}, "advice": "We are asked to find the opportunity cost of forgoing a cash discount, therefore we will use the formula
\n$\\displaystyle \\text{Opportunity Cost}=\\frac{\\text{% discount}}{100- \\text{% discount}}\\times \\frac{365}{\\text{days difference between early and late settlement}}$
\nIn our situation we have,
\n$\\text{% discount}=\\var{a}$,
\n$\\text{days difference between early and late settlement}=\\var{lt}-\\var{et}=\\var{lt-et}$,
\nand therefore we have
\n$\\displaystyle \\text{Opportunity Cost}=\\frac{\\var{a}}{100- \\var{a}}\\times \\frac{365}{\\var{lt-et}}$
\nwhich upon calculation gives
\n$\\begin{align} \\text{Opportunity Cost}&\\approx\\var{OCdec}\\\\&=\\var{OCrounded}\\%\\quad \\text{(to two decimal places)}\\end{align}$
", "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/"}]}