// Numbas version: exam_results_page_options {"name": "Junlei's copy of worksheet 3(Securities and Capital Gains Tax)", "extensions": [], "custom_part_types": [{"source": {"pk": 1, "author": {"name": "Christian Lawson-Perfect", "pk": 7}, "edit_page": "/part_type/1/edit"}, "name": "Yes/no", "short_name": "yes-no", "description": "
The student is shown two radio choices: \"Yes\" and \"No\". One of them is correct.
", "help_url": "", "input_widget": "radios", "input_options": {"correctAnswer": "if(eval(settings[\"correct_answer_expr\"]), 0, 1)", "hint": {"static": true, "value": ""}, "choices": {"static": true, "value": ["Yes", "No"]}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nif(studentanswer=correct_answer,\n correct(),\n incorrect()\n)\n\ninterpreted_answer:\nstudentAnswer=0\n\ncorrect_answer:\nif(eval(settings[\"correct_answer_expr\"]),0,1)", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "if(studentanswer=correct_answer,\n correct(),\n incorrect()\n)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "studentAnswer=0"}, {"name": "correct_answer", "description": "", "definition": "if(eval(settings[\"correct_answer_expr\"]),0,1)"}], "settings": [{"name": "correct_answer_expr", "label": "Is the answer \"Yes\"?", "help_url": "", "hint": "An expression which evaluates totrue
or false
.", "input_type": "mathematical_expression", "default_value": "true", "subvars": false}], "public_availability": "always", "published": true, "extensions": []}], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "ungrouped_variables": ["tax", "tax1", "interest", "interest1", "i2", "price", "a210", "price1", "a22", "reverse", "i2b", "v1", "interest3", "tax4", "tax5", "years", "netReturn", "price2", "price3", "a215", "i2c", "Lyears", "a2L", "i2d", "price4", "price5", "netRed", "tax6", "nyear", "nyearL", "v6", "vnet"], "variables": {"a215": {"definition": "((1-(1/(1+5/100))^15)/{i2c})", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "a215"}, "vnet": {"definition": "1/(1+{netRed}/100)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "vnet"}, "i2b": {"definition": "((sqrt(1+({interest1}/100)))-1)2", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "i2b"}, "tax6": {"definition": "random(25..35#5)", "group": "Ungrouped variables", "description": "", "templateType": "randrange", "name": "tax6"}, "price2": {"definition": "(0.75){interest3}{a215}+100(1/1.05)^15", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "price2"}, "a210": {"definition": "(1-(1/(1+{interest}/100)^10))/{i2}", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "a210"}, "price4": {"definition": "5((1-{v6}^20)/0.06)+100{v6}^20", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "price4"}, "tax5": {"definition": "{tax4}+15", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "tax5"}, "tax4": {"definition": "random(20..30#5)", "group": "Ungrouped variables", "description": "", "templateType": "randrange", "name": "tax4"}, "a2L": {"definition": "((1-(1/(1+{netReturn}/100))^{Lyears})/{i2d})", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "a2L"}, "v6": {"definition": "1/(1+6/100)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "v6"}, "tax1": {"definition": "random(47..42#1)", "group": "Ungrouped variables", "description": "", "templateType": "randrange", "name": "tax1"}, "interest": {"definition": "random(7..9#1)", "group": "Ungrouped variables", "description": "", "templateType": "randrange", "name": "interest"}, "i2": {"definition": "(sqrt(1+({interest}/100))-1)*2", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "i2"}, "reverse": {"definition": "1-({tax1}/100){v1}", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "reverse"}, "price1": {"definition": "((1-({tax1}/100))1000{a22}+11000{v1}-({tax1}/100)(11000){v1})/{reverse}", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "price1"}, "v1": {"definition": "(1/(1+{interest1}/100))^2", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "v1"}, "nyear": {"definition": "random(5..15#5)", "group": "Ungrouped variables", "description": "", "templateType": "randrange", "name": "nyear"}, "interest3": {"definition": "random(3..6#1)", "group": "Ungrouped variables", "description": "", "templateType": "randrange", "name": "interest3"}, "price5": {"definition": "((1-{tax6}/100)5((1-{vnet}^{nyearL})/({netRed}/100))+70{vnet}^{nyearL})/(1-({tax6}/100){vnet}^{nyearL})", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "price5"}, "price3": {"definition": "((1-{tax4}/100){interest3}{a2L}+60(1/(1+{netReturn}/100))^{Lyears})/(1-0.4(1/(1+{netReturn}/100))^{Lyears})", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "price3"}, "nyearL": {"definition": "20-{nyear}", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "nyearL"}, "price": {"definition": "(1-{tax}/100)(1000){a210}+11000(1/((1+{interest}/100)^10))", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "price"}, "a22": {"definition": "((1-(1/(1+{interest1}/100))^2)/{i2b})", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "a22"}, "years": {"definition": "random(7..8#1)", "group": "Ungrouped variables", "description": "", "templateType": "randrange", "name": "years"}, "i2d": {"definition": "((sqrt(1+({netReturn}/100)))-1)2", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "i2d"}, "tax": {"definition": "random(23..27#1)", "group": "Ungrouped variables", "description": "", "templateType": "randrange", "name": "tax"}, "netRed": {"definition": "random(6.5..8#0.5)", "group": "Ungrouped variables", "description": "", "templateType": "randrange", "name": "netRed"}, "i2c": {"definition": "((sqrt(1+(5/100)))-1)2", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "i2c"}, "netReturn": {"definition": "random(6..7#1)", "group": "Ungrouped variables", "description": "", "templateType": "randrange", "name": "netReturn"}, "Lyears": {"definition": "15-{years}", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "Lyears"}, "interest1": {"definition": "{interest}-2", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "interest1"}}, "name": "Junlei's copy of worksheet 3(Securities and Capital Gains Tax)", "rulesets": {}, "extensions": [], "advice": "$P=DNa_{\\bar{n}| i}^{(p)}+RNv_{i}^{n}$
\n$\\frac{C(t)}{R(t)}=\\frac{Q(t)}{Q(b)}$
\n$i^{(p)}\\geq (1-t_1)\\frac{D}{R}$ => Capital Gains Exist
\n$P=(1-t_1)DNa_{\\bar{n}| i}^{(p)}+RNv_{i}^{n}$
\n$P=(1-t_1)DNa_{\\bar{n}| i}^{(p)}+RNv_{i}^{n}-t_2(RN-P)v_{i}^{n}$
\n", "type": "question", "tags": [], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": ""}, "functions": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "statement": "Reminder: To check whether CGT is applicable.
", "parts": [{"prompt": "Ten million pounds nominal of loan stock was issued on 1 January 2006. The stock is due to be redeemed in one payment of 110% nominal on 1 January 2016. The stock pays interest at 10% per annum, payable half-yearly in arrears on 1 June and 1 January.
\na) An investory, subject to income tax at {tax}% but no liable to capital gains tax, bought £10,000 nominal of the stock at issue so as to obtain a net effective yield of {interest}% per annum, after tax. What price did the investor pay per £100 nominal on the date of issue? £[[0]]
\nb) On 1 January 2014, the first inventor, having received the interest due on that date, sold the stock to a second investor who was subject to {tax1}% tax on both income and capital gains. The price paid by the second investor was calculated so as to earn him a net effective yield of {interest1}% per annum, after tax. What price did the second investor pay per £100 nominal? £[[1]]
", "gaps": [{"correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "customMarkingAlgorithm": "", "showCorrectAnswer": true, "maxValue": "{Price}+1", "minValue": "{Price}-1", "variableReplacementStrategy": "originalfirst", "type": "numberentry", "mustBeReduced": false, "extendBaseMarkingAlgorithm": true, "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "marks": 1, "unitTests": [], "variableReplacements": [], "showFeedbackIcon": true, "allowFractions": false, "scripts": {}}, {"correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "customMarkingAlgorithm": "", "showCorrectAnswer": true, "maxValue": "{price1}+0.5", "minValue": "{price1}-0.5", "variableReplacementStrategy": "originalfirst", "type": "numberentry", "mustBeReduced": false, "extendBaseMarkingAlgorithm": true, "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "marks": 1, "unitTests": [], "variableReplacements": [], "showFeedbackIcon": true, "allowFractions": false, "scripts": {}}], "customMarkingAlgorithm": "", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "marks": 0, "variableReplacements": [], "unitTests": [], "sortAnswers": false, "scripts": {}}, {"prompt": "\nInvestor A purchased a bond with exactly 15 years to redemption. The bond is redeemable at par and has a gross redemption yield of 5% per annum effective. It pays coupons of {interest3}% per annum, half-yearly in arrears. He pays tax at 25% on the coupons only.
\na)Calculate the price paid by the investor A for the bond. £[[0]].
\nb)After exactly {years} years, immediately after the payment of the coupon then due, investor A sells this bond to investor B who pays income tax at a rate of {tax4}% and capital gains tax at a rate of {tax5}}%. The bond is purchased by investor B to provide a net return of {netReturn}% per annum effective. Calculate the price paid by investor B. £[[1]].
\n", "gaps": [{"correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "customMarkingAlgorithm": "", "showCorrectAnswer": true, "maxValue": "{price2}+0.5", "minValue": "{price2}-0.5", "variableReplacementStrategy": "originalfirst", "type": "numberentry", "mustBeReduced": false, "extendBaseMarkingAlgorithm": true, "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "marks": 1, "unitTests": [], "variableReplacements": [], "showFeedbackIcon": true, "allowFractions": false, "scripts": {}}, {"correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "customMarkingAlgorithm": "", "showCorrectAnswer": true, "maxValue": "{price}+0.5", "minValue": "{price3}-0.5", "variableReplacementStrategy": "originalfirst", "type": "numberentry", "mustBeReduced": false, "extendBaseMarkingAlgorithm": true, "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "marks": 1, "unitTests": [], "variableReplacements": [], "showFeedbackIcon": true, "allowFractions": false, "scripts": {}}], "customMarkingAlgorithm": "", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "marks": 0, "variableReplacements": [], "unitTests": [], "sortAnswers": false, "scripts": {}}, {"prompt": "An investor purchased a bond with exactly 20 years to redemption. The bond, redeemable at par, has a gross redemption yielf of 6%. It pays annual coupons, in arrears, of 5%. The investor does not pay tax.
\na)Calculate the purchase price paid for the bond. £[[0]]
\nb)After exactly {nyear} years, immediately after payment of the coupon that due, this investor sells the bond to another investor. That investor pays income and capital gains tax at a rate of {tax6}%. The bond is purchased by the second investor to provide a net rate of return of {netRed}% per annum.
\nI) Is CGT applicable?
\n[[2]]
\nII) Calculate the price paid by the second investor. £[[1]]
\n\n\n", "gaps": [{"correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "customMarkingAlgorithm": "", "showCorrectAnswer": true, "maxValue": "{price4}+0.5", "minValue": "{price4}-0.5", "variableReplacementStrategy": "originalfirst", "type": "numberentry", "mustBeReduced": false, "extendBaseMarkingAlgorithm": true, "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "marks": 1, "unitTests": [], "variableReplacements": [], "showFeedbackIcon": true, "allowFractions": false, "scripts": {}}, {"correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "customMarkingAlgorithm": "", "showCorrectAnswer": true, "maxValue": "{price5}+0.5", "minValue": "{price5}-0.5", "variableReplacementStrategy": "originalfirst", "type": "numberentry", "mustBeReduced": false, "extendBaseMarkingAlgorithm": true, "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "marks": 1, "unitTests": [], "variableReplacements": [], "showFeedbackIcon": true, "allowFractions": false, "scripts": {}}, {"extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "showFeedbackIcon": true, "marks": 1, "variableReplacements": [], "unitTests": [], "settings": {"correct_answer_expr": "true"}, "variableReplacementStrategy": "originalfirst", "type": "yes-no", "scripts": {}}], "customMarkingAlgorithm": "", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "marks": 0, "variableReplacements": [], "unitTests": [], "sortAnswers": false, "scripts": {}}], "preamble": {"css": "", "js": ""}, "contributors": [{"name": "Swa Lup", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2902/"}, {"name": "Junlei Hu", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3534/"}]}]}], "contributors": [{"name": "Swa Lup", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2902/"}, {"name": "Junlei Hu", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3534/"}]}