Question

An investor wishes to sell a 30 year $40,000 (face value) bond that matures in seven years. the bond pays semiannual dividends at interest rate of 4% per year ( coupon rate)

A. what should be the selling price of the bond if the buyer plans to hold the bond to maturity and wishes to make 6% per year (nominal) rate of return on the investment?

B. if the bond sells for that price ( value from A) what effective rate of return will the buyer realize ( state interest rate to two decimals)

Answer 1

Ans. Face value, F = $40000

Time to maturity, T = 30 years = 60 semi annual periods

Semi annual Coupon payment, C = Semiannual Coupon Rate * Face Value = 2%*40000 = $800

Semi annual interest rate, r = 6/2 = 3%

Price of bond, P = C*(P/A, 3%, 60) + F/(P/F, 3%, 60) = 800*[(1-1/(1+0.03)^60)/0.03] + 40000/(1+0.03)^60

=> P = $28929.77

Thus, price of the bond is $28929.77

b) Effective annual rate of return, R = (1+r)^2 - 1 = (1+0.03)^2 - 1 = 0.0609 or 6.09%