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Date Submitted: 07/04/2012 01:01 PM
Solutions to Chapter 4
The Time Value of Money
Note: Unless otherwise stated, assume that cash flows occur at the end of each year.
1. a. 100/(1.08)10 = $46.32
b. 100/(1.08)20 = $21.45
c. 100/(1.04)10 = $67.56
d. 100/(1.04)20 = $45.64
3. With simple interest, you earn 4% of $1000, or $40 each year. There is no interest on interest. After 10 years, you earn total interest of $400, and your account accumulates to $1400. With compound interest, your account grows to 1000 ( (1.04)10 = $1480. Therefore $80 is interest on interest.
5.
Present Value Years Future Value Interest Rate*
a. $400 11 $684 5% = ()1/11 – 1
b. $183 4 $249 8% = ()1/4 – 1
c. $300 7 $300 0% = ()1/7– 1
To find the interest rate, we rearrange the equation
FV = PV ( (1 + r)n to conclude that r = ()1/n - 1
To use a financial calculator for (a) enter PV= (-)400, FV = 684, PMT = 0, n = 11
and compute the interest rate.
7. PV = 200/1.05 + 400/1.052 + 300/1.053
= 190.48 + 362.81 + 259.15 = $812.44
9. a. PV = 100 × PVIFA(.08,10) = 100 × 6.7101 = 671.01
b. PV = 100 × PVIFA(.08,20) = 100 × 9.8181 = 981.81
c. PV = 100 × PVIFA(.04,10) = 100 × 8.1109 = 811.09
d. PV = 100 × PVIFA(.04,20) = 100 × 13.5903 = 1,359.03
|11. | | | |Per Period Rate, | |
| | | | |APR/m | |
| | |APR |Compounding Period | |Effective annual rate |
| | | | | | |
| |a. |12% |1 month (m = 12/yr) |.12/12...