Question

1. Assume that you will deposit $4000 at the end of each of the next three years in a St. George bank account paying 8% interest. You currently have $7000 in the account. How much will you have in three years? In four years?

2. You are looking into an investment that will pay you $12,000 per year for the next 10 years. If you require a 15% return, what is the most you would pay for this investment?

3. A bond has an 8% coupon, paid semi-annually. The face value is $100, and the bond matures in 6 years. If the bond currently sells for $91.137, what is the yield to maturity? What is the effective annual yield?

Answer 1

Answer to Question 1:

Current balance = $7,000
Annual Deposit = $4,000
Interest Rate = 8%

Balance after 3 years = $7,000*1.08^3 + $4,000*1.08^2 + $4,000*1.08 + $4,000
Balance after 3 years = $21,803.58

Balance after 4 years = $21,803.58*1.08
Balance after 4 years = $23,547.87

Answer to Question 2:

Annual Payment = $12,000
Period = 10 years
Annual Interest Rate = 15%

Cost of Investment = $12,000/1.15 + $12,000/1.15^2 + $12,000/1.15^3 + ... + $12,000/1.15^10
Cost of Investment = $12,000 * (1 - (1/1.15)^10) / 0.15
Cost of Investment = $60,225.22

Maximum amount paid for the investment is $60,225.22

Answer to Question 3:

Face Value = $100
Current Price = $91.137

Annual Coupon Rate = 8%
Semiannual Coupon Rate = 4%
Semiannual Coupon = 4% * $100
Semiannual Coupon = $4

Time to Maturity = 6 years
Semiannual Period to Maturity = 12

Let semiannual YTM be i%

$91.137 = $4 * PVIFA(i%, 12) + $100 * PVIF(i%, 12)

Using financial calculator:
N = 12
PV = -91.137
PMT = 4
FV = 100

I = 5%

Semiannual YTM = 5%
Annual YTM = 2 * 5% = 10%

Effective Annual Yield = (1 + Semiannual YTM)^2 - 1
Effective Annual Yield = (1 + 0.05)^2 - 1
Effective Annual Yield = 1.1025 - 1
Effective Annual Yield = 0.1025 or 10.25%