A 16-year, 4.5 percent coupon bond pays interest annually. The bond has a face value of $1,000. What is the percentage change in the price of this bond if the market yield to maturity rises to 5.7 percent from the current rate of 5.5 percent?

2.2% change in the price of this bond if the market yield to maturity rises to 5.7 percent from the current rate of 5.5 percent.

Explanation:

Face Value = $1,000

Coupon payment = 1000 x 4.5% = $45 annually

Number of periods = n = 16 years

Price of bond is the present value of future cash flows, to calculate Price of the bond use following formula

Price of the Bond = C x [ (1 - (1 + r) ^-n) / r ] + [ F / (1 + r) ^n ]

Yield to maturity = 5.7%

Price of the Bond = $45 x [ (1 - (1 + 5.7%) ^-16) / 5.7% ] + [ $1,000 / (1 + 5.7%) ^16 ]

Price of the Bond = $876.18

Yield to maturity = 5.5%

Price of the Bond = $45 x [ (1 - (1 + 5.5%) ^-16) / 5.5% ] + [ $1,000 / (1 + 5.5%) ^16 ]

Price of the Bond = $895.38

Percentage Change = ($895.38 - $876.18) / $876.18 = 2.2%