Question

Suppose a 15-year bond with $100 face value, 8.00% coupon rate and semiannual coupons is currently trading at par. All else constant, if the yield to maturity of the bond suddenly changes to 7.00% APR, what will happen to this bond’s price?

Group of answer choices

it will decrease by $9.108

it will decrease by $8.745

it will increase by $9.196

it will stay the same

Answer 1

Since the bond is trading at par, current price = $100

Semi annaul coupon = [(8 / 100) * 100] / 2 = 4

Number of periods = 15 * 2 = 30

Semi annual rate = 7% / 2 = 3.5%

new price = Coupon * [1 - 1 / (1 + rate)^time] / rate + Face value / (1 + rate)^time

new price = 4 * [1 - 1 / (1 + 0.035)^30] / 0.035 + 10 / (1 + 0.035)^30

new price = 4 * [1 - 0.35628] / 0.035 + 35.62784

new price = 4 * 18.39205 + 35.62784

new price = $109.196

Change in price = $109.196 - $100

Change in price = $9.196

it will increase by $9.196