On January 1, 2016, a company issued $400,000 of 10-year, 12% bonds. The interest is payable semi-annually on June 30 and December 31. The issue price was $413,153 based on a 10% market interest rate. The effective-interest method of amortization is used. The interest expense for the six-month period ending December 31, 2016 is closest to:
A)$24,000.
B)$20,491.
C)$20,000.
D)$20,825.

Question

Quizplus · Accepted Answer

First, we need to calculate the semi-annual interest payment:
$400,000 x 12% x 6/12 = $24,000

Then, we need to calculate the semi-annual interest expense using the effective-interest method of amortization. We start by calculating the effective interest rate:
PV of bond = $413,153
Payment amount = $24,000
n = 20 (number of semi-annual periods)
Solve for i:
PV of bond = Payment amount x (1 - (1 + i)^-n)/i + FV x (1 + i)^-n
$413,153 = $24,000 x (1 - (1 + i)^-20)/i + $0 x (1 + i)^-20
i = 5.92%

Using this effective interest rate, we can calculate the interest expense for the first six months:
Carrying value at issuance = $413,153
Interest expense = Carrying value x Effective interest rate = $413,153 x 5.92% = $24,425

Therefore, the closest answer choice is B) $20,491, which represents half of the total interest expense for the year.

On January 1, 2016, a Company Issued $400,000 of 10-Year