a bond has 8 years to maturity, annual interest payments, par value of 1000, coupon rate of 9 percent and YTM of 7 percent

Time to maturity = 8 years | Par value = 1000 | Coupon rate = 9%

Annual Coupon = Coupon rate * 1000 = 9% * 1000 = 90

First we will calculate the Price of Bond at YTM of 7%

Price of a bond = Annual Coupon * (1 - (1 + YTM)^-T) / YTM + Par value / (1 + YTM)^T

Putting values, Price of the bond at 7% YTM = 90 * (1 - (1 + 7%)^-8) / 7% + 1000 / (1 + 7%)⁸

= 90 * 5.9713 + 582.01

= 537.42 + 582.01

Hence, Price of the bond at 7% YTM = 1,119.43

Now we will calculate the Price of bond at YTM of 8%

Price of a bond = Annual Coupon * (1 - (1 + YTM)^-T) / YTM + Par value / (1 + YTM)^T

Putting values, Price of the bond at 8% YTM = 90 * (1 - (1 + 8%)^-8) / 8% + 1000 / (1 + 8%)⁸

= 90 * 5.7466 + 540.27

= 517.20 + 540.27

Hence, Price of the bond at 8% YTM = 1,057.47

Percentage Change in Price of bond = (Price at New YTM - Price at Old YTM) / Price at Old YTM

Percentage Change in Price of bond = (Price at 8% YTM - Price at 7% YTM) / Price at 7% YTM

= (1,057.47 - 1,119.43) / 1,119.43

= -61.96 / 1,119.43

Hence, Percentage Change in Price of bond = -5.53% (Negative sign shows decline in price)