On january 1, 2023, discount tire issued $500,000, 6%, 10-year bonds for $581,771. the bonds pay interest semi-annually on june 30 and december 31. the market rate of interest is 4%. what is the amount of cash interest paid for the year ended december 31, 2023?

Question: On january 1, 2023, discount tire issued $500,000, 6%, 10-year bonds for $581,771. the bonds pay interest semi-annually on june 30 and december 31. the market rate of interest is 4%. what is the amount of cash interest paid for the year ended december 31, 2023?

To calculate the amount of cash interest paid for the year ended December 31, 2023, we need to determine the amount of interest expense Discount Tire has accrued for the year.

Discount Tire issued $500,000, 6%, 10-year bonds at a premium, meaning the market rate of interest is lower than the bond's stated rate. We can use the effective interest method to calculate the interest expense.

The annual interest payment for the bond is ($500,000 x 6%) = $30,000. However, since the bonds were issued at a premium, Discount Tire will pay less than this amount in cash interest.

The premium on the bonds is the difference between the face value ($500,000) and the amount received from issuing the bonds ($581,771), which is $81,771. This premium will be amortized over the life of the bond using the effective interest method.

The semi-annual interest payment is ($30,000 / 2) = $15,000. The effective interest rate is calculated as the market rate plus the premium amortization divided by the carrying value of the bond. The carrying value of the bond at the end of the year is the face value of the bond ($500,000) plus the premium amortization ($81,771 - ($81,771 / 20)) = $524,104.

The effective interest rate for the first interest payment on June 30, 2023, is (($15,000 / $524,104) * 2) = 5.74%. The effective interest rate for the second interest payment on December 31, 2023, is (($15,000 / $524,104) * 2) = 5.78%.

The interest expense for the year is the sum of the interest accrued for each semi-annual payment, or ($15,000 x 2) = $30,000. Therefore, the amount of cash interest paid for the year ended December 31, 2023, is $30,000.