Question

Twenty-five $1.000 bonds having a bond rate of 8% per year payable quar- terly are purchased for $22,500 and kept for 5 years. Assume that the bonds are sold immediately after receiving the coupon payments at the end of the 5th year. What must they be sold for in order to earn a 6% effective annual return on the investment?

Answer 1

Total face value of bonds ($) = 25 x 1,000 = 25,000

Total quarterly bond coupon ($) = 25,000 x 8% x (1/4) = 500

Number of quarters = 4 x 5 = 20

Quarterly (nominal) interest rate = 6%/4 = 1.5%

Selling price ($) = 500 x F/A(1.5%, 20) + 22,500 x F/P(1.5%, 20)

= 500 x 23.1237** + 22,500 x 1.3469**

= 11,561.85 + 30,305.25

= 41,867.10

F/A(1.5%, 20) = [(1.015)²⁰ - 1] / 0.015 = (1.3469 - 1) / 0.015 = 0.3469 / 0.015 = 23.1237

F/P(1.5%, 20) = (1.015)²⁰ = 1.3469