ch02-Actsc231 - Chapter 2. Equations of Value and Yield...

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Chapter 2. Equations of Value and Yield RatesACTSC231 — Mathematics of FinanceDepartment of Statistics and Actuarial ScienceUniversity of WaterlooFall 2010Instructor: Chengguo WengC. Weng ([email protected])– p. 1/1
Simple Eq. of ValueEq. of value with a single payment:AK(T) =K(1 +i)TXBoxK——investment amount/capital/contribution made at time 0XBoxAK(T)——accumulated value at timeTXBoxT——length of investment periodXBox(annual) effective interest rateExample 2.1:Anita’s aunt opens an account and deposits$Cfor her. Theaccount earns compound interest with an annual effective interest rate of 8%.Five years after the account was open, Anita closes the account and received$3,673.32. FindC.C. Weng ([email protected])– p. 2/1
Simple Eq. of ValueExample 2.2:Anita deposits$400in an account that grows by compoundinterest. After 5 years the balance has grown to$463.71. What’s the annualeffective interest rate this account earns?C. Weng ([email protected])– p. 3/1
Simple Eq. of ValueExample 2.3:John borrows $1,000. The loan is governed by compound interestat an annual effective interest rate of 10%. John repays $600 at the end of theone year and plan to complete repayment of the loan with a payment of$Patthe end of the second year. FindP.Consider time 0, time 1 and time 2 equations of value respectively.C. Weng ([email protected])– p. 4/1
General eq. of valueRefer back to e.g. 2.3 in the previous slide. We can regard the money Johnholds pertaining the loan as a fund, and every income and outgo amount can bethought of as a contribution to the fund, so that an income yields a positivecontribution while an outgo results in a negative contribution. Then, if{Ctk,k= 0,1,· · ·,n}is the sequence of contributions with eachCtkmade attimetk, the time 0 equation of value becomesnsummationdisplayk=0Ctk·vtk= 0.

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Term
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WILKIE

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