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ACTSC 231 ch04-Actsc231

# ACTSC 231 ch04-Actsc231 - Chapter 4 Annuities with...

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Chapter 4. Annuities with different payment and conversion periods 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 3

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Example 4.1 Example 4.1: Suppose an annuity pays \$1000 every 5 years for 35 years. The rate of interest is 5% per year effective. Find the present value and the accumulation value at the expiration date for a) payments in advance; b) payments in arrear. C. Weng ([email protected]) – p. 2/1 3
Payments less frequent than interest is compounded Consider an annuity that makes a payment of \$P every m periods for nm periods. Thus, there are n payments in total. Assume the effective interest is i for each payment period. Evaluation method 1: find the effective interest rate (denoted by j ) for m periods first. X payable in arrear: PV = P · a n j , AV = P · s n j X payable in advance: PV = P · ä n j , AV = P · ¨s n j Evaluation method 2: X payable in arrear: PV = P · a nm s m or = P · ä nm ¨s m ; AV = P · s nm s m or = P · ¨s nm ¨s m X payable in advance: PV = P · a nm a m or = P · ä nm ä m ; AV = P · s nm a m or = P · ¨s nm ä m C. Weng ([email protected]) – p. 3/1 3

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Example 4.2 Example 4.2: Suppose an annuity pays \$100 every month for 15 years. The
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ACTSC 231 ch04-Actsc231 - Chapter 4 Annuities with...

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