Gunther Inc.purchased $400,000 of Malone Corp.ten-year bonds with a stated interest rate of 8 percent payable quarterly.At the time the bonds were purchased,the market interest rate was 12 percent.Determine the amount of premium or discount on the purchase of the bonds.

Question

Quizplus · Accepted Answer

When the market interest rate is higher than the stated interest rate, the bond is sold at a discount. To determine the discount, we need to calculate the present value of the bond's cash flows using the market interest rate of 12 percent. The bond pays interest quarterly, so the semi-annual market rate is 6 percent. Using the formula for present value of an annuity, we get:

P = (C/r)[1 - 1/(1+r)^n] + FV/(1+r)^n
P = (20,000/0.06)[1 - 1/(1.06)^40] + 400,000/(1.06)^40
P = $307,558.08

The purchase price of the bond was $400,000, so we subtract the present value from the face value to get the discount:

Discount = $400,000 - $307,558.08 = $92,441.92

Therefore, the answer is B) $92,442 discount (rounded to the nearest cent).