Final answer:
To calculate the interest expense recognized in 2024 using the effective-interest method of amortization, multiply the bond's book value by the market rate of interest. Adjust the book value for subsequent calculations based on the difference between interest expense and actual interest paid.
Step-by-step explanation:
The question asks how to calculate the interest expense recognized in 2024 for a company that issued $15,000,000 in bonds at 7.8%, with an effective interest rate of 8%, using the effective-interest method of amortization. Using this method, the interest expense for a period is determined by multiplying the book value of the bonds at the beginning of the period by the market interest rate (yield rate) at the time the bonds were issued.
For the first payment, we take the initial book value of $14,703,120 and multiply it by the semi-annual market rate of 4% (half of 8% since interest is paid semi-annually) to obtain the interest expense for the first six months. The book value will then be adjusted based on the difference between the actual cash paid (bond coupon rate times principal) and the interest expense calculated.
The process is then repeated for the subsequent payment period, with the new book value being used to calculate the next interest expense. Throughout 2024, these calculations will be done twice (June 30 and December 31).