Mermaid Inc.sold a $50,000, 8%, 5-year bond for $46,139 to yield 10%.Interest is paid semi-annually.The net carrying value of the bond after the first interest payment will be closest to:

Question

Quizplus · Accepted Answer

The semi-annual coupon payment is $50,000 x 8% x 1/2 = $2,000.
Using the formula for present value of an annuity, the price of the bond is:
Price = $2,000 x [1 - 1/(1+0.05)^10]/0.05 + $50,000/(1+0.05)^10
Price = $46,139
Since the bond was sold at a discount, its net carrying value will increase after the first interest payment. The first interest payment will be $2,000 x 10% = $200.
Therefore, the net carrying value after the first interest payment will be $46,139 + $200 = $46,339, which is closest to option A ($46,446).