Chapter 10 Solution

35 for the next 15 years pv 1432471 pmt 1000 i

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Unformatted text preview: rst calculate the PV, 15 years from now, of the last 10 years’ payments of PMT = \$1500/month with j = 5%, m = 1, c = 11 = 0.08 3 , n = 12(10) = 120, and 2 i2 = (1 + i ) c − 1 = (1.05) 0.083 – 1 = 0.00407412378 1 − 1.00407412378 −120 = \$142,148.386 PV = \$1500 0.00407412378 Next determine the combined PV of this amount and the first 15 years’ payments of PMT = \$1000/month with the same i2 and n = 12(15) = 180. 1 − 1.00407412378 −180 \$142,148.386 PV = + \$1000 0.00407412378 1.0515 = \$68,375.804 + \$127,385.158 = \$195,760.96 5 I/Y P/Y 12 ENTER C/Y 1 ENTER 120 N 1500 PMT 0 FV CPT PV Ans: –142,148.386 Same I/Y, P/Y, C/Y 180 N 1000 PMT 142148.386 FV CPT PV Ans: –195,760.96 Exercise 10.5 (continued) 33. Value of contract = PV of all payments First calculate the PV, 2½ years from now, of the last 3½ years’ payments of PMT = \$2000/quarter with j = 6%, m = 2, c = 2 = 0.5, n = 4(3.5) = 14, and 4 0.5 i2 = (1 + i ) c − 1 = (1.03) – 1 = 0.0148891565 1 − ( 1 + i ) − n 1 − 1.0148891565 −14 PV = PMT = \$2000 0.0148891565 i = \$25,106.659 Next determine the combined PV of this amount and the first 2½ years’ payments of PMT = \$500/month j = 6%, m = 2, c = 2 12 = 0.16 , n = 12(2.5) = 30, and i2 = (1 + i ) c − 1 = (1.03) 0.16 – 1 = 0.00493862203 1 − 1.00493862203 −30 \$25,106.659 + \$500 0.00493862203 1.0049386220330 = \$35,567.10 PV = 6 I/Y P/Y 4 ENTER C/Y 2 ENTER 14 N 2000 PMT 0 FV CPT PV Ans: –25,106.659 Same I/Y P/Y 12 ENTER C/Y 2 ENTER 30 N 500 PMT 25106.659 FV CPT PV Ans: –35,567.10 35. The inheritance's current economic value is the present value of the deferred general annuity. Since the first quarterly payment is 4.5 years from now, the period of deferral is 4.25 years (if we wish to treat the payments as a deferred ordinary annuity). 6 I/Y Given: PMT = \$2000, n = 4(20) = 80, P/Y 4 ENTER 12 6% C/Y 12 ENTER d = 4(4.25) = 17, i = 12 = 0.5%, c = 4 = 3 80 N i2 = (1 + i ) c − 1 = (1.005 ) 3 – 1 = 0.015075125 2000 PMT 0 FV Chapter 10: Ordinary Annuities: Future Value and Present Value 75 CPT PV Ans: −92...
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