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**Unformatted text preview: **.5
Number of payments per year
4
i2 = (1 + i ) c − 1 = (1.045 ) 0.5 – 1 = 0. 022252415 1.022252415 20 − 1 FV = $400 0.022252415 = $9939.94 9 I/Y P/Y 2 ENTER (making C/Y = P/Y)
16 N 5000 PV 0 PMT
CPT FV Ans: −10,111.85 Same I/Y, PV P/Y 4 ENTER C/Y 2 ENTER 20 N 400 PMT
CPT FV Ans: −9939.94 Exercise 10.5 (continued)
19. The amount required to purchase the annuity is the present value of
the payments discounted at the rate of return on the annuity.
PMT = $2500, n = 12(20) = 240, i = 6.75%,
Number of compoundin gs per year
6.75 I/Y 1
c=
=
= 0.08 3 P/Y 12 ENTER Number of payments per year
12 C/Y 1 ENTER c
0.08 3
– 1 = 0.00545813044
i2 = (1 + i ) − 1 = = (1.0675 )
240 N 1 − ( 1 + i ) − n 2500 PMT
PV = PMT 0 FV i CPT PV 1 − 1.0054581304 4 −240 Ans: −333,998.96 = $2500 0.0054581304 4 = $333,998.96
21. Selling price = Down payment + Present value of the monthly payments
Given: PMT = $259.50; n = 12(3.5) = 42.
7.5 I/Y Then
i = 7.5% = 7.5%, c = 11 = 0.083 , and
2
1 P/Y 12 ENTER i2 = (1 + i ) c − 1 = (1.075) 0.083 – 1 = 0.0060449190 C/Y 1 ENTER 1 − ( 1 + i ) − n 42 N PV = PMT 259.50 PMT
i 0 FV CPT PV 7/e
70
Business Mathematics in Canada, Ans: –9600.00 1 − 1.006044919 −42 = $259.50 0.006044919 = $9600.00
Thus, the selling price was $2000 + $9600.00 = $11,600.00. Chapter 10: Ordinary Annuities: Future Value and Present Value 71 Exercise 10.5 (continued)
23. a. Plan A: Total contributions = 480($100) = $48,000
Plan B: Total contributions = 360($200) =$72,000
Plan C: Total contributions = 240($400) =$96,000
Therefore, A : B : C = 48 : 72 : 96 = 2 : 3 : 4
b. Comparing future values,
A : B : C = $421,924 : $340,423 : $255,541
= 1.65 : 1.33 : 1
25. For the first 10 years, i = 6%
12 = 0.5%; PMT = $1500; n = 2(10) = 20; c = 12
2 = 0.16 6 I/Y P/Y 2 ENTER C/Y 12 ENTER 20 N 0 PV 1500 + / – PMT
CPT FV Ans: 40,460.694 – 1 = 0.030377509
i2 = (1 + i ) − 1 = (1.005)
and the future value at the end of the 8.5years is (1 + i ) n − 1
FV = PMT i c 0.16 1.030377509 20...

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