Question

You are considering a 10-year, $1000 par value bond. It’s coupon rate is 11%, and interest is paid semiannually. If you require an “effective” annual interest rate (not a nominal rate) of 11.61%, 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 Interest Rate = 11.61%

Effective Annual Interest Rate = (1 + Semiannual Interest Rate)^2 - 1
0.1161 = (1 + Semiannual Interest Rate)^2 - 1
1.1161 = (1 + Semiannual Interest Rate)^2
1.0565 = 1 + Semiannual Interest Rate
Semiannual Interest Rate = 0.0565 or 5.65%

Face Value = $1,000

Annual Coupon Rate = 11%
Semiannual Coupon Rate = 5.50%
Semiannual Coupon = 5.50% * $1,000
Semiannual Coupon = $55

Time to Maturity = 10 years
Semiannual Period = 20

Price of Bond = $55 * PVIFA(5.65%, 20) + $1,000 * PVIF(5.65%, 20)
Price of Bond = $55 * (1 - (1/1.0565)^20) / 0.0565 + $1,000 / 1.0565^20
Price of Bond = $982.30

So, you should pay $982.30 for this bond.