Question

In February 2015, Treasury offered a semiannually compounded 4.8% 25-year bond with yield to maturity of 2.60% (annual rate). The par value is $1,000. Recognizing that coupons are paid semiannually,

a) Calculate the bond's price as of February 2015.

b) Calculate the bond's price as of February 2020 (everything else stays the same)

Answer 1

Par Value = $1,000

Annual Coupon Rate = 4.80%
Semiannual Coupon Rate = 2.40%
Semiannual Coupon = 2.40% * $1,000
Semiannual Coupon = $24

Annual YTM = 2.60%
Semiannual YTM = 1.30%

Answer a.

Time to Maturity = 25 years
Semiannual Period = 50

Price of Bond = $24 * PVIFA(1.30%, 50) + $1,000 * PVIF(1.30%, 50)
Price of Bond = $24 * (1 - (1/1.013)^50) / 0.013 + $1,000 * (1/1.013)^50
Price of Bond = $24 * 36.597148 + $1,000 * 0.524237
Price of Bond = $1,402.57

Answer b.

Time to Maturity = 20 years
Semiannual Period = 40

Price of Bond = $24 * PVIFA(1.30%, 40) + $1,000 * PVIF(1.30%, 40)
Price of Bond = $24 * (1 - (1/1.013)^40) / 0.013 + $1,000 * (1/1.013)^40
Price of Bond = $24 * 31.037221 + $1,000 * 0.596516
Price of Bond = $1,341.41