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n = 2(17) = 34, i = 6.4%
2 8 I/Y P/Y 1 ENTER (making C/Y = P/Y = 1)
3 N 0 PV 1000 + / – PMT
CPT FV Ans: 3246.40 6.4 I/Y P/Y 2 ENTER (making C/Y = P/Y = 2)
34 N 0 PV 1000 + / – PMT
CPT FV Ans: 59,942.63 = 3.2% (1 + i ) n − 1
FV = PMT i 34 1.032 − 1
= $1000 0.032 = $59,942.63
The client’s investments are worth $59,942.63 today.
15. a. Given: PMT = $500, n = 4(20) = 80, i = 8%
4 = 2% 1.02 80 − 1 (1 + i ) n − 1 FV = PMT = $500 0.02 = $96,885.98
i b. If, instead, i = 10%
4=
80 2.5% 1.025 − 1 FV = $500 0.025 = $124,191.36 Exercise 10.2 (continued)
17. The amount 5 years from now will be the combined future value of the
$20,000 already saved and the annual $5000 contributions. That is, (1 + i ) n − 1
n FV = PV ( 1 + i ) + PMT i 1.0725 5 − 1 = $20,000 (1.0725 ) 5 + $5000 0.0725 = $28,380.27 + $28,897.48
= $57,277.75 44 Business Mathematics in Canada, 7/e Exercise 10.2 (continued)
19. For the first 2 years, PMT = $1200,
n = 2(4) = 8, i = 10% = 2.5%.
4
The future value after 2 years is (1 + i ) n − 1
FV = PMT i 1.025 8 − 1 = $1200 0.025 = $10,483.34 10 I/Y P/Y 4 ENTER (making C/Y = P/Y = 4)
8 N 0 PV 1200 + / – PMT
CPT FV Ans: 10,483.34 For the next 3 years, n = 4(3) = 12,
%
PV = $10,483.34, PMT = $1200, i = 94 = 2.25%
The combined future value of these amounts
at the end of the 3 years is (1 + i ) n − 1
FV = PMT + PV (1 + i ) n
i Same P/Y, C/Y, PMT
9 I/Y 12 N 10483.34 + / – PV CPT FV Ans: 30,014.43 1.022512 − 1 12 = $1200 0.0225 + $10,483.34 (1.0225 ) = $16,322.67 + $13,691.77
= $30,014.43
21. After 10 years, Marika's RRSP will be worth (1 + i ) n − 1 + PMT FV = PV (1 + i )
i 1.045 20 − 1 = $18,000 (1.045 ) 20 + $2000 0.045 = $43,410.85 + $62,742.85
= $106,153.70
(continued)
n 9 I/Y P/Y 2 ENTER (making C/Y = P/Y = 2)
20 N 18000 + / – PV 2000 + / – PMT
CPT FV Ans: 106,153.70 Chapter 10: Ordinary Annuities: Future Value and Present Value 45 Exercise 10.2 (continued)
21. (continued)
After a further 5 years, the RRSP will be worth 1.0075 60 − 1 FV = $106,153.70 (1.0075 ) 60 + $300 0.0075 = $166,202.834 + $22,627.241
= $188,830.08 25...

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