Question

You are considering a 20-year, $1,000 par value bond. Its coupon rate is 8%, and interest is paid semiannually.

Open spreadsheet If you require an "effective" annual interest rate (not a nominal rate) of 10.86%, 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

r = semi annual rate

(1+r)^2 - 1 = 10.86%

1+r = 1.05290075505

r = 5.29%

Par value = $1,000

C = semi annual coupon = $1,000 * 8% /2 = $40

n = 20*2 = 40 semi annual compoundings

Present value of bond = [C * [1 - (1+r)^-n] / r] + [Par value / (1+r)^n]

= [$40 * [1 - (1+5.29%)^-40] / 5.29%] + [$1,000 / (1+5.29%)^40]

= [$40 * 0.87279183949 / 0.0529] + [$1,000 /7.86113088997]

= $659.956022303 + $127.208160505

= $787.164182808

Therefore, value of bond today is $787.16