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Unformatted text preview: 1 = $1500 0.030377509 = $40,460.694 For the next 15 years, PMT = $1500; 1 n = 2(15) = 30; i = 7% = 7%; c = 2 = 0.5 1 0.5 i2 = (1 + i ) c − 1 = (1.07) – 1 = 0.024695077 The combined future value at the end of the 25 years is 1.024695077 30 − 1 $40,460.694 (1.07) 15 + $1500 0.024695077 = $111,632.330 + $76,684.027 = $188,316.36 Same PMT, P/Y 7 I/Y C/Y 1 ENTER 30 N 40460.694 + / – PV CPT FV Ans: 188,316.36 Exercise 10.5 (continued) 27. For the first 10 years, i = PMT = $1000; n = 10; c = 7.5% 12 12 1 = 0.625%; 7.5 I/Y P/Y 1 ENTER C/Y 12 ENTER 10 N 0 PV 1000 + / – PMT CPT FV Ans: 14,324.71 = 12 i2 = (1 + i ) − 1 = (1.00625 ) 12 – 1 = 0.077632599 (1 + i ) n − 1 FV = PMT i 1.077632599 10 − 1 = $1000 0.077632599 – 1 = $14,324.71 c and Same PMT, P/Y 8 I/Y C/Y 2 ENTER 15 N 14324.71 + / – PV Business Mathematics in Canada, 7/e CPT FV Ans: 73,953.35 For the next 15 years, PV = $14,324.71; PMT = $1000; i = 8% = 4%; c = 2 = 2; n = 15 1 2 72 and i2 = (1 + i ) c − 1 = (1.04 ) 2 – 1 = 0.0816 The combined future value after 25 years will be 15 − 1 30 + $1000 1.0816 $14,324.71 (1.04 ) 0.0816 = $73,953.35 Chapter 10: Ordinary Annuities: Future Value and Present Value 73 Exercise 10.5 (continued) 29. For the past 9 years, % i = 84 = 2%; PMT = $2000; n = 9; c = 4 = 4; and 1 i2 = (1 + i ) c − 1 = (1.02) 4 – 1 = 0.082432160 The current value of Gloria's RRSP is (1 + i ) n − 1 FV = PMT i 1.08243216 9 − 1 = $2000 0.08243216 – 1 = $25,230.137 For the next 15 years, PMT = $2000; n = 30; i = 2%; c = 4 = 2; PV = $25,230.137; 2 and i2 = (1 + i ) c − 1 = (1.02) 2 – 1 = 0.0404 The total amount 15 years from now will be 1.0404 30 − 1 60 $25,230.137 (1.02) + $2000 0.0404 = $195,703.17 74 8 I/Y P/Y 1 ENTER C/Y 4 ENTER 9 N 0 PV 2000 + / – PMT CPT FV Ans: 25,230.137 Same I/Y, PMT P/Y 2 ENTER C/Y 4 ENTER 30 N 25230.137 + / – PV CPT FV Ans: 195,703.17 Business Mathematics in Canada, 7/e Exercise 10.5 (continued) 31. Cost to purchase the annuity = PV of all payments Fi...
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