Question

Question 3 20 pts A firm has issued $1,000 bonds with a 3% coupon interest rate paid semi- annually. The bonds mature 10 years from now and may be purchased for $800 each. What effective annual rate of return would you receive if you purchased the bond now and held it to maturity 10 years from now? Submit your answer in decimal form. EX: Submit 0.05 if the answer if 5 Margin of error: +/- 0.003

Answer 1

coupon payment = 3% * 1000 / 2 = 15 per semiannual period

Let rate of return received per semiannual period is i%

-800 + 15* (P/A, i%,20) + 1000 * (P/F, i%,20) = 0

15* (P/A, i%,20) + 1000 * (P/F, i%,20) = 800

Dividing by 5

3* (P/A, i%,20) + 200 * (P/F, i%,20) = 160

using trail and error method

when i = 2%, value of 3* (P/A, i%,20) + 200 * (P/F, i%,20) = 183.648567

when i = 3%, value of 3* (P/A, i%,20) + 200 * (P/F, i%,20) = 155.367575

using interpolation

i = 2% + (183.648567 - 160) / (183.648567 - 155.367575 ) *(3%-2%)

i = 2% + 0.836%

i = 2.836% = 2.84%

i = 0.0284

Effective annual rate of return = (1+0.0284)^2 - 1 = 1.057606 - 1 = 0.0576 (Answer)