Question

Three $1,000, 8% coupon rate bonds have 2,10 and 20 years until maturity respectively. If interest rates move up to 10%, the following bond prices will occur: $828.36, $964.54, and $875.39. Which term goes with which price?

two years/$875.39, 10 years/$964.54, 20 years/$828.36

two years/$964.54, 10 years/$875.39, 20 years/$828.36

two years/$875.39, 10 years/$828.36, 20 years/$964.54

two years/$964.54, 10 years/$828.36, 20 years/$875.36

Answer 1

Bond 1:

Face Value = $1,000

Annual Coupon Rate = 8%
Semiannual Coupon Rate = 4%
Semiannual Coupon = 4% * $1,000
Semiannual Coupon = $40

Time to Maturity = 2 years
Semiannual Period = 4

Annual Interest Rate = 10%
Semiannual Interest Rate = 5%

Price of Bond = $40 * PVIFA(5%, 4) + $1,000 * PVIF(5%, 4)
Price of Bond = $40 * (1 - (1/1.05)^4) / 0.05 + $1,000 / 1.05^4
Price of Bond = $964.54

Bond 2:

Face Value = $1,000

Annual Coupon Rate = 8%
Semiannual Coupon Rate = 4%
Semiannual Coupon = 4% * $1,000
Semiannual Coupon = $40

Time to Maturity = 10 years
Semiannual Period = 20

Annual Interest Rate = 10%
Semiannual Interest Rate = 5%

Price of Bond = $40 * PVIFA(5%, 20) + $1,000 * PVIF(5%, 20)
Price of Bond = $40 * (1 - (1/1.05)^20) / 0.05 + $1,000 / 1.05^20
Price of Bond = $875.39

Bond 3:

Face Value = $1,000

Annual Coupon Rate = 8%
Semiannual Coupon Rate = 4%
Semiannual Coupon = 4% * $1,000
Semiannual Coupon = $40

Time to Maturity = 20 years
Semiannual Period = 40

Annual Interest Rate = 10%
Semiannual Interest Rate = 5%

Price of Bond = $40 * PVIFA(5%, 40) + $1,000 * PVIF(5%, 40)
Price of Bond = $40 * (1 - (1/1.05)^40) / 0.05 + $1,000 / 1.05^40
Price of Bond = $828.36