a
", "definition": "100((1-{v2})/{d2}-10{v2})/({rate}/100)"}, "int5": {"name": "int5", "templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "(({value1}/1000)^(1/5)-1)*100"}, "y": {"name": "y", "templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "(100000-100{sn1}{abc})/({sn1}{abc}+{sn2})"}, "int1": {"name": "int1", "templateType": "randrange", "group": "Ungrouped variables", "description": "", "definition": "random(7..8#1)"}, "total": {"name": "total", "templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "{value2}{v}^4 + {value3}{v}^7 + {value4}{v}^13"}, "value7": {"name": "value7", "templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "{value}-250"}, "d2": {"name": "d2", "templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "({rate}/100)/(1+{rate}/100)"}, "v2": {"name": "v2", "templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "(1/(1+{rate}/100))^10"}, "d": {"name": "d", "templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "0.07/1.07"}, "abc": {"name": "abc", "templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "(1.07)^(42-{year})"}, "value6": {"name": "value6", "templateType": "randrange", "group": "Ungrouped variables", "description": "", "definition": "random(2100..2300#0.01)"}, "rate": {"name": "rate", "templateType": "randrange", "group": "Ungrouped variables", "description": "", "definition": "random(4..7#1)"}, "int3": {"name": "int3", "templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "(({value}/1000)^(1/3)-1)*100"}, "int": {"name": "int", "templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "(({value1}/{value})^(1/2)-1)*100"}, "delta": {"name": "delta", "templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "ln(1+({rate}/100))"}, "sn1": {"name": "sn1", "templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "(((1.07)^{year})-1)/d"}, "value": {"name": "value", "templateType": "randrange", "group": "Ungrouped variables", "description": "", "definition": "random(1250..1350#10)"}, "payment": {"name": "payment", "templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "-{value7}*(1.06)^10+{value6}"}, "repayment1": {"name": "repayment1", "templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "log({value5}/{total})/log(1+{int1}/100)"}, "value8": {"name": "value8", "templateType": "randrange", "group": "Ungrouped variables", "description": "", "definition": "random(10000..20000#5000)"}}, "ungrouped_variables": ["value", "value1", "int3", "int5", "int", "value2", "value3", "value4", "value5", "int1", "repayment", "repayment1", "v", "total", "value6", "interest", "payment", "v10", "value7", "year", "year1", "year2", "year3", "y", "d", "sn1", "sn2", "abc", "value8", "value9", "v1", "x", "reverse", "rate", "arrears", "continuously", "v2", "d2", "delta"], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": ""}, "extensions": [], "variable_groups": [], "preamble": {"css": "", "js": ""}, "functions": {}, "tags": [], "statement": "", "variablesTest": {"condition": "", "maxRuns": 100}, "name": "worksheet 2(cash flows and annuities)", "parts": [{"sortAnswers": false, "marks": 0, "showCorrectAnswer": true, "prompt": "In return for a single payment of £1000, an investment bank offers the following alternatives:
\nA: A lump sum of £{value} after three years,
\nB: A lump sum of £{value1} after five years.
\na)Write down an equation of value for each alternative and find the yield for each.
\nAnswer in %. A: [[0]]%, B: [[1]]%
\n\nb)Assume that an investor selects alternative A and that after three years she invests the proceeds for a further two years at a fixed rate of interest. How large must this rate of interest be in order for her to receive at least £{value1} at the end of 5 years?
\nAnswer in %. [[2]]%
", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "gaps": [{"notationStyles": ["plain", "en", "si-en"], "marks": 1, "showCorrectAnswer": true, "minValue": "{int3}", "maxValue": "{int3}", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "allowFractions": false, "mustBeReduced": false, "unitTests": [], "mustBeReducedPC": 0, "type": "numberentry", "correctAnswerFraction": false, "showFeedbackIcon": true, "correctAnswerStyle": "plain"}, {"notationStyles": ["plain", "en", "si-en"], "marks": 1, "showCorrectAnswer": true, "minValue": "{int5}", "maxValue": "{int5}", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "allowFractions": false, "mustBeReduced": false, "unitTests": [], "mustBeReducedPC": 0, "type": "numberentry", "correctAnswerFraction": false, "showFeedbackIcon": true, "correctAnswerStyle": "plain"}, {"notationStyles": ["plain", "en", "si-en"], "marks": 1, "showCorrectAnswer": true, "minValue": "{int}", "maxValue": "{int}", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "allowFractions": false, "mustBeReduced": false, "unitTests": [], "mustBeReducedPC": 0, "type": "numberentry", "correctAnswerFraction": false, "showFeedbackIcon": true, "correctAnswerStyle": "plain"}], "customMarkingAlgorithm": "", "unitTests": [], "scripts": {}, "showFeedbackIcon": true, "type": "gapfill"}, {"sortAnswers": false, "marks": 0, "showCorrectAnswer": true, "prompt": "A borrower is under an obligation to repay a bank £{value2} in four year's time, £{value3} in seven's year time and £{value4} in thirteen year's time.
\nAs part of a review of his future commitments the borrower now offers either
\nA: To discharge his liability for these three debts by making an appropriate single payment five years from now; or
\nB: To repay the total amount owed (i.e. £{value5} in a single payment at an appropriate future time.)
\nOn the basis of a constant interest rate of {int1}% per annum, find the appropriate single payment if offers A is accepted by the bank, and the appropriate time to repay the entire indebtness if offer B is accepted. (You should work on the basis that the present value of the single payment under the revised arrangement should equal the present value of the three payments due under the current obligation)
\nPayment A:£[[0]], Year B:[[1]]Years
", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "gaps": [{"notationStyles": ["plain", "en", "si-en"], "marks": 1, "showCorrectAnswer": true, "minValue": "{repayment}-0.5", "maxValue": "{repayment}+0.5", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "allowFractions": false, "mustBeReduced": false, "unitTests": [], "mustBeReducedPC": 0, "type": "numberentry", "correctAnswerFraction": false, "showFeedbackIcon": true, "correctAnswerStyle": "plain"}, {"notationStyles": ["plain", "en", "si-en"], "marks": 1, "showCorrectAnswer": true, "minValue": "{repayment1}-0.5", "maxValue": "{repayment1}+0.5", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "allowFractions": false, "mustBeReduced": false, "unitTests": [], "mustBeReducedPC": 0, "type": "numberentry", "correctAnswerFraction": false, "showFeedbackIcon": true, "correctAnswerStyle": "plain"}], "customMarkingAlgorithm": "", "unitTests": [], "scripts": {}, "showFeedbackIcon": true, "type": "gapfill"}, {"sortAnswers": false, "marks": 0, "showCorrectAnswer": true, "prompt": "You borrow £{value7} from a bank at an effective rate of interest of 6% per annum. You invest it in a project which pays £{value6} at the end of ten years.
\n\na) What is your internal rate of return of this project?Answer in %. [[0]]%
\nb) You repay the bank at the end of ten years (repaying the loan and the interest accumulated over the ten years) out of payment from the project. What is your profit at the end of the day? £[[1]]
", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "gaps": [{"notationStyles": ["plain", "en", "si-en"], "marks": 1, "showCorrectAnswer": true, "minValue": "{interest}-0.2", "maxValue": "{interest}+0.2", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "allowFractions": false, "mustBeReduced": false, "unitTests": [], "mustBeReducedPC": 0, "type": "numberentry", "correctAnswerFraction": false, "showFeedbackIcon": true, "correctAnswerStyle": "plain"}, {"notationStyles": ["plain", "en", "si-en"], "marks": 1, "showCorrectAnswer": true, "minValue": "{payment}-1", "maxValue": "{payment}+1", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "allowFractions": false, "mustBeReduced": false, "unitTests": [], "mustBeReducedPC": 0, "type": "numberentry", "correctAnswerFraction": false, "showFeedbackIcon": true, "correctAnswerStyle": "plain"}], "customMarkingAlgorithm": "", "unitTests": [], "scripts": {}, "showFeedbackIcon": true, "type": "gapfill"}, {"sortAnswers": false, "marks": 0, "showCorrectAnswer": true, "prompt": "You plan to accumulate £100,000 at the end of 42 years by making the following deposits:
\nX at the beginning of years 1 to {year},
\nNo deposits at the beginning of years {year1} to {year2}; and
\nY at the beginning of years {year3} to 42.
\nThe annual effective interest rate is 7%. If X-Y=100. Calculate Y. Y=£[[0]]
", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "gaps": [{"notationStyles": ["plain", "en", "si-en"], "marks": "2", "showCorrectAnswer": true, "minValue": "{y}-1", "maxValue": "{y}+1", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "allowFractions": false, "mustBeReduced": false, "unitTests": [], "mustBeReducedPC": 0, "type": "numberentry", "correctAnswerFraction": false, "showFeedbackIcon": true, "correctAnswerStyle": "plain"}], "customMarkingAlgorithm": "", "unitTests": [], "scripts": {}, "showFeedbackIcon": true, "type": "gapfill"}, {"sortAnswers": false, "marks": 0, "showCorrectAnswer": true, "prompt": "An investment requires an initial payment of £{value8} and annual payments of £{value9} at the end of each of the first 10 years. Starting at the end of the eleventh year, the investment returns five equal annual payments of X. Determine X to yield an annual effective rate of 10% over the 15-year period.
\nX=£[[0]]
", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "gaps": [{"notationStyles": ["plain", "en", "si-en"], "marks": 1, "showCorrectAnswer": true, "minValue": "{x}-1", "maxValue": "{x}+1", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "allowFractions": false, "mustBeReduced": false, "unitTests": [], "mustBeReducedPC": 0, "type": "numberentry", "correctAnswerFraction": false, "showFeedbackIcon": true, "correctAnswerStyle": "plain"}], "customMarkingAlgorithm": "", "unitTests": [], "scripts": {}, "showFeedbackIcon": true, "type": "gapfill"}, {"sortAnswers": false, "marks": 0, "showCorrectAnswer": true, "prompt": "Find the present value of a 10 year increasing annuity that pays at an annual rate of 100, 200,... 1000, given that the annual effective interest rate is {rate}% and payments are made:
\na) annual in arrears. £[[0]]
\nb) continuously. £[[1]]
", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "gaps": [{"notationStyles": ["plain", "en", "si-en"], "marks": 1, "showCorrectAnswer": true, "minValue": "{arrears}-1", "maxValue": "{arrears}+1", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "allowFractions": false, "mustBeReduced": false, "unitTests": [], "mustBeReducedPC": 0, "type": "numberentry", "correctAnswerFraction": false, "showFeedbackIcon": true, "correctAnswerStyle": "plain"}, {"notationStyles": ["plain", "en", "si-en"], "marks": 1, "showCorrectAnswer": true, "minValue": "{continuously}-1", "maxValue": "{continuously}+1", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "allowFractions": false, "mustBeReduced": false, "unitTests": [], "mustBeReducedPC": 0, "type": "numberentry", "correctAnswerFraction": false, "showFeedbackIcon": true, "correctAnswerStyle": "plain"}], "customMarkingAlgorithm": "", "unitTests": [], "scripts": {}, "showFeedbackIcon": true, "type": "gapfill"}], "advice": "$NPV= \\sum_{k=1}^{n}C(t_{k})v_{i}^{t_{k}}$
\n$a_{\\bar{n}| i}^{(p)}={(1-v^i) \\over i^p}$
\n$s_{\\bar{n}| i}^{(p)}={(1+i)^n-1 \\over i^{(p)}}=(1+i)^n(a_{\\bar{n}| i}^{(p)})$
\n$s_{\\bar{\\infty}| i}=\\frac{1}{i}$
\n$m|a_{\\bar{n}| i}=v_{i}^{m}(a_{\\bar{n}| i})$
\n$(Ia)_{\\bar{n}| i}=\\frac{\\ddot{a}_{\\bar{n}| i}-nv^n}{i}$
\n$(Is)_{\\bar{n}| i}=(1+i)^n(Ia)_{\\bar{n}| i}$
\n$(Da)_{\\bar{n}| i}=\\frac{n-a_{\\bar{n}| i}}{i}$
", "rulesets": {}, "type": "question", "contributors": [{"name": "Swa Lup", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2902/"}]}]}], "contributors": [{"name": "Swa Lup", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2902/"}]}