// Numbas version: finer_feedback_settings
{"name": "Discounting", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["value", "n", "interest"], "name": "Discounting", "tags": [], "advice": "<p>Discounting is the process of going back in time. In this example, &pound;{value} is the future value and we want the present value of this i.e. the value that will give us &pound;{value} when interest is earned.</p>\n<p>In order to get the present value, we need to use:</p>\n<p style=\"text-align: center;\">$V(0)=V(n)v^n$</p>\n<p>where:</p>\n<ul>\n<li>$V(0)$= value at time 0</li>\n<li>$V(n)$= value at time n</li>\n<li>$v={1 \\over 1+i}$. This is the discount factor.</li>\n</ul>\n<p>As the interest rate that is quoted is the annual effective rate, the time must be in terms of years. So to change months into years, one must divide by 12.</p>\n<p>In the above question, we have:</p>\n<ul>\n<li>$V(n)$= &pound;{value}</li>\n<li>$n$={n} months</li>\n<li>$i$={interest}%</li>\n</ul>\n<p>Substituting these values in to the equation gives the present/discounted value.</p>\n<p></p>", "rulesets": {}, "parts": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "scripts": {}, "precision": "2", "maxValue": "{value}/(1+{interest/100})^{n/12}", "minValue": "{value}/(1+{interest/100})^{n/12}", "strictPrecision": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "marks": "2", "type": "numberentry", "showPrecisionHint": false}], "statement": "<p>Compute the present value of a payment of <strong>&pound;{value}</strong> due in <strong>{n}</strong> months on the basis of a compound interest rate of <strong>{interest}%&nbsp;</strong><em>per annum</em>?</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"value": {"definition": "random(300..900#50)", "templateType": "randrange", "group": "Ungrouped variables", "name": "value", "description": ""}, "interest": {"definition": "random(1..8#0.25)", "templateType": "randrange", "group": "Ungrouped variables", "name": "interest", "description": ""}, "n": {"definition": "random(1..11#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "n", "description": ""}}, "metadata": {"notes": "", "description": "", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Habiba Gora", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/494/"}]}]}], "contributors": [{"name": "Habiba Gora", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/494/"}]}