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Unformatted text preview: 1 = Payment at first annuity period = A/(1+i) PV 2 = A 2 /(1+i) 2 Total present value = PV 1 + PV 2 + PV 3 + . ..+ PV n To make it into a geometric series, add A in front and subtract A from the present value after that PV= A(1(1+i)n )/ i) FV= A((1+i) n1)/i) In class examples 1 a. FV= 120,000 i=9% n= 8 years(matches interest rates) PV=? Single payment today PV= FV/(1+i) 8 = 120,000/(1.09) 8 =60,223.95 b. PV= 120,000(1.05) 8 / (1.09) 8 = 83,973.21 2. PV = 10,000 I nom = 3% C =12 n=42 months FV=? 1. Convert i = i nom /C I= 0.03/12= 0.0025 2. FV= PV(1+) n = 10,000 (1.0025) 42 = 11,105.65 3. Ordinary annuity PV= ? A= $2,250 per year I= 10% per year N= 15 years Note compounding frequency = payment frequency for annuities PV= 2250 x (1(1.1)15 )/0.10)= 17,113.68 4. Deposits are monthly, means compounded monthly FV= A[(1+i) n1/i] x (1+i) = 200[(1+0.07/12) 1801/(0.07/12)] x (1+0.07)= 63,762.25...
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This note was uploaded on 03/30/2008 for the course ORIE 350 taught by Professor Callister during the Spring '08 term at Cornell.
 Spring '08
 CALLISTER

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