Question

Suppose a ten year, $1,000 bond with an 8.4 % coupon rate and semiannual coupons is trading for $1034.66.

a. What is the bond's yield to maturity (expressed as an APR with semiannual compounding)

b. if the bond's yield to maturity changes to 9.7% APR, what will be the bond's price.

Answer 1

a)

Coupon = (8.4% of 1000) / 2 = 42

Number of periods = 10 * 2 = 20

Yield to maturity = 7.89%

Keys to use in a financial calculator:

2nd P/Y 2

FV 1000

PV -1034.66

N 20

PMT 42

CPT I/Y

2)

Rate = 9.7% / 2 = 4.85%

Bond's price = Coupon * [1 - 1 / (1 + r)^n] / r + FV / (1 +r)^n

Bond's price = 42 * [1 - 1 / (1 + 0.0485)^20] / 0.0485 + 1000 / (1 +0.0485)^20

Bond's price = 42 * [1 - 0.387821] / 0.0485 + 387.820984

Bond's price = 42 * 12.622247 + 387.820984

Bond's price = $917.96