ch02-Actsc231 - Chapter 2 Equations of Value and Yield Rates ACTSC231 Mathematics of Finance Department of Statistics and Actuarial Science University

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

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Chapter 2. Equations of Value and Yield Rates ACTSC231 — Mathematics of Finance Department of Statistics and Actuarial Science University of Waterloo Fall 2010 Instructor: Chengguo Weng C. Weng ([email protected]) – p. 1/1
Simple Eq. of Value Eq. of value with a single payment: A K ( T ) = K (1 + i ) T XBox K ——investment amount/capital/contribution made at time 0 XBox A K ( T ) ——accumulated value at time T XBox T——length of investment period XBox (annual) effective interest rate Example 2.1: Anita’s aunt opens an account and deposits $ C for her. The account 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. Find C . C. Weng ([email protected]) – p. 2/1
Simple Eq. of Value Example 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?
Simple Eq. of Value Example 2.3: John borrows $1,000. The loan is governed by compound interest at an annual effective interest rate of 10%. John repays $600 at the end of the one year and plan to complete repayment of the loan with a payment of $ P at the end of the second year. Find P . Consider time 0, time 1 and time 2 equations of value respectively. C. Weng ([email protected]) – p. 4/1
General eq. of value Refer back to e.g. 2.3 in the previous slide. We can regard the money John holds pertaining the loan as a fund, and every income and outgo amount can be thought of as a contribution to the fund, so that an income yields a positive contribution while an outgo results in a negative contribution. Then, if { C t k ,k = 0 , 1 , · · · ,n } is the sequence of contributions with each C t k made at time t k , the time 0 equation of value becomes n summationdisplay k =0 C t k · v t k = 0 .

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