Question

Question 7 2 points Save Answer Bond P is a premium bond with a coupon of 8 percent, a YTM of 6.58 percent, and 19 years to maturity. Bond D is a discount bond with a coupon of 8 percent, a YTM of 9.66 percent, and also 19 years to maturity. If interest rates remain unchanged, what is the difference in the prices of these bonds 9 year from now? (i.e., Price of Bond P- Price of Bond D) Note: Corporate bonds pay coupons twice a year. (Input all amounts as positive values. Do not round intermediate calculations. Round your answers to 2 decimal places.)

Answer 1

Bond P:

Face Value = $1,000

Annual Coupon Rate = 8.00%
Semiannual Coupon Rate = 4.00%
Semiannual Coupon = 4.00% * $1,000
Semiannual Coupon = $40

Time to Maturity = 10 years
Semiannual Period = 20

Annual YTM = 6.58%
Semiannual YTM = 3.29%

Price in 9 years from now = $40 * PVIFA(3.29%, 20) + $1,000 * PVIF(3.29%, 20)
Price in 9 years from now = $40 * (1 - (1/1.0329)^20) / 0.0329 + $1,000 / 1.0329^20
Price in 9 years from now = $1,102.85

Bond D:

Face Value = $1,000

Annual Coupon Rate = 8.00%
Semiannual Coupon Rate = 4.00%
Semiannual Coupon = 4.00% * $1,000
Semiannual Coupon = $40

Time to Maturity = 10 years
Semiannual Period = 20

Annual YTM = 9.66%
Semiannual YTM = 4.83%

Price in 9 years from now = $40 * PVIFA(4.83%, 20) + $1,000 * PVIF(4.83%, 20)
Price in 9 years from now = $40 * (1 - (1/1.0483)^20) / 0.0483 + $1,000 / 1.0483^20
Price in 9 years from now = $895.06

Difference in Bond Price = $1,102.85 - $895.06
Difference in Bond Price = $207.79