Consider three bonds with 520 coupon rates all making annual

Consider three bonds with 5.20% coupon rates, all making annual coupon payments and all selling at face value. The short-term bond has a maturity of 4 years, the intermediate-term bond has a maturity of 8 years, and the long-term bond has a maturity of 30 years

a. What will be the price of the 8-year bond if its yield decreases to 4.20%? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

b. What will be the price of the 30-year bond if its yield decreases to 4.20%? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Solution

Answer a.

Face Value = $1,000

Annual Coupon Rate = 5.20%
Annual Coupon = 5.20% * $1,000
Annual Coupon = $52

Time to Maturity = 8 years
Annual Yield to Maturity = 4.20%

Price of Bond = $52 * PVIFA(4.20%, 8) + $1,000 * PVIF(4.20%, 8)
Price of Bond = $52 * (1 - (1/1.042)^8) / 0.042 + $1,000 / 1.042^8
Price of Bond = $1,066.77

Answer b.

Face Value = $1,000

Annual Coupon Rate = 5.20%
Annual Coupon = 5.20% * $1,000
Annual Coupon = $52

Time to Maturity = 30 years
Annual Yield to Maturity = 4.20%

Price of Bond = $52 * PVIFA(4.20%, 30) + $1,000 * PVIF(4.20%, 30)
Price of Bond = $52 * (1 - (1/1.042)^30) / 0.042 + $1,000 / 1.042^30
Price of Bond = $1,168.80