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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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