Question

Suppose a 5-year bond with a 5% coupon rate, semiannual coupons and a face value of $1000 has a yield to maturity of 8% APR.

1. What is the bond’s yield to maturity expressed as an effective semi-annual rate? What is the bond’s yield to maturity expressed as an effective annual rate (EAR)?

2. What is the price of the bond?

3. If the bond’s yield to maturity changes to 5% APR, what will the bond’s price be?

Answer 1

Yield to maturity expressed as an effective semi-annual rate = APR/2 = 8%/2 = 4%

EAR = (1 + 0.08/2)^2 - 1

EAR = 0.0816

EAR = 8.16%

FV = 1,000

cpn = 1,000 * 0.05/2 = 25

r = 8%/2 = 0.04

n = 5 * 2 = 10 semi-annual payments

Bond's price with 8% APR yield to maturity is $878.3365633258

If the yield to maturity is changed to 5% APR, then...

r = 5%/2 = 0.025

Bond's price with an yield to maturity of 5% APR is $1,000