Finance Lecture _2 - k denote the balance in the account...

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MAT 183 Math of Finance Lecture #2 Nov. 23/24, 2009 1 Math of Finance Lecture #2 Annuities § 10.2 Review of basics: Problems 17, 18, 24, 26 (pg 477-9) An annuity is a sequence of regular payments called the rent and denoted by R ; the payment periods and the compounding periods are the same ; and payments are made at the end of each period. Increasing annuities: Let B k denote the balance in the account just after the end of the k th pay- ment/compounding period: B k = (1 + i ) B k - 1 + R B 0 = 0; B 1 = R ; B 2 = (1 + i ) R + R ; B 3 = (1 + i ) B 2 + R = (1 + i ) 2 R + (1 + i ) R + R ; B n = (1 + i ) n - 1 R + · · · + (1 + i ) 2 R + (1 + i ) R + R ; B n = ± (1 + i ) n - 1 + · · · + (1 + i ) 2 + (1 + i )+1 ² R ; F = ³ (1+ i ) n - 1 i ´ R = s n | i R. Decreasing annuities: Let B
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Unformatted text preview: k denote the balance in the account just after the end of the k th pay-ment/compounding period: B k = (1 + i ) B k-1 + R B = P ; B 1 = (1 + i ) P-R ; B 2 = (1 + i ) B 1-R = (1 + i ) 2 P-(1 + i ) R-R ; B n = (1+ i ) n P-(1+ i ) n-1 R-(1+ i ) n-2 R--R ; 0 = (1+ i ) n P- (1 + i ) n-1 + (1 + i ) n-2 + + 1 R ; 0 = (1+ i ) n P- (1+ i ) n-1 i R or P = (1+ i ) n-1 i (1+ i ) n R = a n | i R. Work problems 3, 5, 8, 13, 17, 18, 21, 22, 24, 26, 27, 28, 39, 46, 47 (pg 487-9)...
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