# Week 3 Homework Fin 6000

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Week 3 Assignment 1
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1. Calculating the Number of Periods
At 8 percent interest, how long does it take to double your money? To quadruple it?

FV = PV (FVF) 8%, t = ?
\$2 = \$1 (FVF) 8%, t = ?
\$2/ 1 = 2.0; so for FVF at 8 %, “t” is approximately 9 years.

2. Perpetuities
An investor purchasing a British consul is entitled to receive annual payments from the British government forever. What is the price of a consul that pays \$160 annually if the next payment occurs one year from today? The market interest rate is 4.5 percent.

PV = C / r
PV = \$160 / 0.045
PV = \$3,555.56

3. Present Value and Multiple Cash Flows
Investment X offers to pay you \$6,000 per year for nine years, whereas Investment Y offers to pay you \$8,500 per year for ﬁve years. Which of these cash ﬂow streams has the higher present value if the discount rate is 9 percent? If the discount rate is 21 percent?

PVA = C ({1 – [1/(1 + r)]^t} / r
X @ 9%: PVA \$6,000 {[1 – (1 / 1.09)^9] / .09} = \$35,974.48
Y @ 9%: PVA \$8,500 {[1 – (1/1.09)^5] / .09} = \$33,062.04

X @ 21%: PVA \$6,000 {[1 – (1 / 1.21)^9] / .21} = \$23,432.61
Y @ 21%: PVA \$8,500 {[1 – (1/1.21)^5] / .21} = \$24,870.87

4. Calculating EAR First National Bank charges 15.1 percent compounded monthly on its business loans. First United Bank charges 15.5 percent compounded semiannually. As a potential borrower, which bank would you go to for a new loan?

EAR = [1 + (APR / m)]^m – 1

First National: EAR = [1 + (0.151 / 12)]^12 – 1 = 0.1619 – 16.19%
First United: EAR = [1 + (0.155 / 2)]^2 – 1 = 0.1510 – 16.10%

5. Calculating Annuities
You are planning to save for retirement over the next 30 years. To do this, you will invest \$700 a month in a stock account and \$300 a month in a bond account. The return of the stock account is expected to be 11 percent, and the bond...

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