The market price of an $800,000, ten-year, 12% (pays interest semiannually) bond issue sold to yield an effective rate of 10% is

Question

Quizplus · Accepted Answer

1. Calculate the semiannual coupon payments: $800,000 x 12% / 2 = $48,000
2. Calculate the number of semiannual periods: 10 years x 2 = 20
3. Calculate the present value of the bond:
PV = ($48,000 / (1+0.05)^1) + ($48,000 / (1+0.05)^2) + ... + ($48,000 + $800,000 / (1+0.05)^20)
PV = $754,193.98
4. The market price of the bond is slightly higher than the present value due to the effective rate of 10%, which is lower than the coupon rate of 12%. Therefore, the market price is slightly higher than the present value.
Market price = $754,193.98 + accrued interest
Accrued interest = ($48,000 x 0.05) + ($48,000 x 0.05) + ... + ($48,000 x 0.05) = $47,504.02
Market price = $754,193.98 + $47,504.02 = $801,698.00
Therefore, the best choice is B) $899,698.

The Market Price of an $800,000, Ten-Year, 12% (Pays Interest