Question

You are considering a 20-year, $1,000 par value bond. Its coupon rate is 8%, and interest is paid semiannually. If you require an "effective" annual interest rate (not a nominal rate) of 11.14%, how much should you be willing to pay for the bond? Do not round intermediate steps. Round your answer to the nearest cent.

Answer 1

Effective Annual Rate = 11.14%
(1 + Semiannual Interest Rate)^2 - 1 = 0.1114
(1 + Semiannual Interest Rate)^2 = 1.1114
1 + Semiannual Interest Rate = 1.05423
Semiannual Interest Rate = 0.05423 or 5.423%

Face Value = $1,000

Annual Coupon Rate = 8.00%
Semiannual Coupon Rate = 4.00%
Semiannual Coupon = 4.00% * $1,000
Semiannual Coupon = $40

Time to Maturity = 20 years
Semiannual Period = 40

Price of Bond = $40 * PVIFA(5.423%, 40) + $1,000 * PVIF(5.423%, 40)
Price of Bond = $40 * (1 - (1/1.05423)^40) / 0.05423 + $1,000 / 1.05423^40
Price of Bond = $769.33

So, you should pay $769.33 for this bond.