Question

1. (Coupon bond price) Consider a 20 year bond that sells at face value (its price is equal to the final payment you get for it in 20 years). The nominal interest rate is expected to be fixed at 4% and is equal to the implicit rate on the bond. i) How much is the coupon rate of the bond? What is the coupon rate if instead the bond matures in 35 years? ii) Now consider the general case in which the price and face value of the bond may be different and the nominal interest rate is given by i. Write down the formula to compute the price of a bond that matures in 5 years.

That's the entire question

Answer 1

(i)

When a bond's selling price equals its face value, the bond's coupon rate is always equal to the nominal interest rate, irrespective of maturity period. So, when maturity is 20 years and 35 years, the bond's coupon rate is 4% in both cases.

(ii)

If coupon payment per year be $C, selling price be $P and face value be $F, then

P = [C / (1 + i)] + [C / {(1 + i)²}] + [C / {(1 + i)³}] + [C / {(1 + i)⁴}] + [C / {(1 + i)⁵}] + [F / {(1 + i)²}]