Question

A treasury bond with a face value of $5 000 and coupon rate of 6% payable semi-annually was bought when the market’s nominal rate was 9%. The bond matures 20 years from now. What do you pay for the bond?

Answer 1

Solution:

Given,
Coupon rate = 6 % * 6 / 12
= 3 % (Semi-annual coupon rate).

Time period for the maturity of bond = 20 * 12 / 6
  = 40 Semi-annual time periods.

Yield to maturity (YTM) on bond = 9 % * 6 / 12
  = 4.5 % (Semi-annual market interest rate).

=> Price of bond = Present value of coupon (interest) on bond + Present value of principal on bond.
=> Price of bond = 5000 * 3 % * [ 1 - (1.045)^-40 ] / 0.045 + 5000 / (1.045)⁴⁰
=> Price of bond = 150 * (1 - 0.1719) / 0.045 + 5000 / 5.81636
=> Price of bond = $ 3619.977 (Rounded off to $ 3620)

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