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{"name": "MATH1510 Financial Mathematics 1 Practical 4B", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {"accum1": {"definition": "var cells = [20];\n\nfor (i=0; i<m30+1; i++) {\n  var int;\n  if(i<=n30) {\n    int=int1d;\n  } else {\n    int=int2d;\n  }\n  var accum = ((1+int)*cells[i]) + 20;\n  cells.push(accum);\n}\n\nreturn cells;", "type": "list", "parameters": [["m30", "number"], ["n30", "number"], ["int1d", "number"], ["int2d", "number"]], "language": "javascript"}}, "ungrouped_variables": ["m", "m30", "int1", "int2", "n", "n30", "int1d", "int2d", "value", "value1", "accum1", "test"], "name": "MATH1510 Financial Mathematics 1 Practical 4B", "tags": [], "advice": "<p style=\"padding-left: 30px;\">1. In order to change the force of interest to the interest rate per day, $i_{[365]}$, remember that:</p>\n<p style=\"text-align: center;\">$(1+i_{[365]})^{365}=e^\\delta$</p>\n<p style=\"padding-left: 30px;\">2. In order to get the accumulated salary at the end of a certain day, you must multiply the salary of the previous day by the interest and then add on the current day salary:</p>\n<p style=\"text-align: center;\">$salary\\ of\\ previous\\ day(1+i_{[365]})+20$</p>\n<p style=\"padding-left: 30px;\">3. In order to determine the salary that will give a cetrain amount at the end of the internship, it is best to try trial and error or use the bisection method.</p>", "rulesets": {}, "parts": [{"precisionType": "dp", "prompt": "<p><span>What is $i_{[360]}$ (% to five decimal places) if $\\delta$={int1*100}%</span></p>", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "5", "maxValue": "{int1d}*100", "minValue": "{int1d}*100", "variableReplacementStrategy": "originalfirst", "strictPrecision": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "scripts": {}, "marks": "2", "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "prompt": "<p><span>What is $i_{[360]}$ (% five decimal places) if $\\delta$={int2*100}%</span></p>", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "5", "maxValue": "{int2d}*100", "minValue": "{int2d}*100", "variableReplacementStrategy": "originalfirst", "strictPrecision": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "scripts": {}, "marks": "2", "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "prompt": "<p>Construct an Excel spreadhsheet that shows the accumulated salary at the end of each day. Create it in such a way that the salary can be changed by hand so that part g) can be solved easily.&nbsp;</p>\n<p>What is the accumulated salary (to two decimal places) at the end of day {{30*n}-4}?</p>", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "accum1[n30-5]", "minValue": "accum1[n30-5]", "variableReplacementStrategy": "originalfirst", "strictPrecision": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "scripts": {}, "marks": "10", "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "prompt": "<p><span>What is the accumulated salary (to two decimal places)&nbsp;at the end of day {{30*m}-15}?</span></p>", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "(accum1[m30-16])+0.3", "minValue": "(accum1[m30-16])-0.3", "variableReplacementStrategy": "originalfirst", "strictPrecision": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "scripts": {}, "marks": "10", "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "prompt": "<p>What is the accumulated salary&nbsp;(to two decimal places) at the end of the internship?</p>", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "(accum1[m30-1])+0.3", "minValue": "(accum1[m30-1])-0.3", "variableReplacementStrategy": "originalfirst", "strictPrecision": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "scripts": {}, "marks": "10", "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "prompt": "<p>What is the sum of salaries (to two decimal places)&nbsp;corresponding to days {n30-15}, {n30-14},..., {n30+15}?</p>", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "{test}+5", "minValue": "{test}-5", "variableReplacementStrategy": "originalfirst", "strictPrecision": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "scripts": {}, "marks": "20", "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "prompt": "<p>What salary (to two decimal places)&nbsp;should the intern be offered in order to accumulate &pound;{value1} (up to &pound;0.01) over {m} months?</p>\n<p><button id=\"#btn\" onclick=\"\n  if (document.getElementById('showhide').style.display == 'block')\n    {document.getElementById('showhide').style.display = 'none';}\n  else\n    {document.getElementById('showhide').style.display = 'block';}\">Hint</button></p>\n<div id=\"showhide\" style=\"display: none;\">\n<ul>\n<li>Adapt your Excel spreadsheet and use Excel Solver.</li>\n<li>Alternatively, apply a bisection method by hand (see <a href=\"https://en.wikipedia.org/wiki/Bisection_method\">Bisection Method</a>).</li>\n</ul>\n</div>", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "({value1}/accum1[m30-1])*20", "minValue": "({value1}/accum1[m30-1])*20", "variableReplacementStrategy": "originalfirst", "strictPrecision": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "scripts": {}, "marks": "5", "type": "numberentry", "showPrecisionHint": false}], "statement": "<p>An intern is paid &pound;20 a day for {m} months (={30*m} days). The force of interest $\\delta$ is {int1*100}% in the first {n} months (={30*n} days) and $\\delta$={int2*100}% in the final {m-n} month(s).</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"n30": {"definition": "30*{n}", "templateType": "anything", "group": "Ungrouped variables", "name": "n30", "description": ""}, "m": {"definition": "random([3,4,5])", "templateType": "anything", "group": "Ungrouped variables", "name": "m", "description": ""}, "int2d": {"definition": "(e^({int2}/360))-1", "templateType": "anything", "group": "Ungrouped variables", "name": "int2d", "description": ""}, "value": {"definition": "precround((accum1[m30-1]*1.25),4)\n", "templateType": "anything", "group": "Ungrouped variables", "name": "value", "description": ""}, "n": {"definition": "{m}-2", "templateType": "anything", "group": "Ungrouped variables", "name": "n", "description": ""}, "int1d": {"definition": "(e^({int1}/360))-1", "templateType": "anything", "group": "Ungrouped variables", "name": "int1d", "description": ""}, "int1": {"definition": "random(0.04..0.06#0.005)", "templateType": "randrange", "group": "Ungrouped variables", "name": "int1", "description": ""}, "value1": {"definition": "precround(accum1[m30-1]*1.25,0)", "templateType": "anything", "group": "Ungrouped variables", "name": "value1", "description": ""}, "int2": {"definition": "random(0.01..0.03#0.005)", "templateType": "randrange", "group": "Ungrouped variables", "name": "int2", "description": ""}, "test": {"definition": "accum1[n30-16]+accum1[n30-15]+accum1[n30-14]+accum1[n30-13]+accum1[n30-12]+accum1[n30-11]+accum1[n30-10]+accum1[n30-9]+accum1[n30-8]+accum1[n30-7]+accum1[n30-6]+accum1[n30-5]+accum1[n30-4]+accum1[n30-3]+accum1[n30-2]+accum1[n30-1]+accum1[n30]+accum1[n30+1]+accum1[n30+2]+accum1[n30+3]+accum1[n30+4]+accum1[n30+5]+accum1[n30+6]+accum1[n30+7]+accum1[n30+8]+accum1[n30+9]+accum1[n30+10]+accum1[n30+11]+accum1[n30+12]+accum1[n30+13]+accum1[n30+14]\n", "templateType": "anything", "group": "Ungrouped variables", "name": "test", "description": ""}, "m30": {"definition": "{m}*30", "templateType": "anything", "group": "Ungrouped variables", "name": "m30", "description": ""}, "accum1": {"definition": "accum1(m30,n30,int1d,int2d)", "templateType": "anything", "group": "Ungrouped variables", "name": "accum1", "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": "James Fung", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/699/"}]}]}], "contributors": [{"name": "James Fung", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/699/"}]}