A company issues $5,000,000, 7.8%, 20-year bonds to yield 8% on January 1, 2010.Interest is paid on June 30 and December 31.The proceeds from the bonds are $4,901,036.Using effective-interest amortization, how much interest expense will be recognized in 2010?

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Quizplus · Accepted Answer

Using effective-interest amortization, the interest expense recognized in 2010 can be calculated as follows:
Step 1: Calculate the annual interest payment:
Annual interest payment = Face value of bonds × Coupon rate
= $5,000,000 × 7.8% = $390,000
Step 2: Calculate the semiannual interest payment:
Semiannual interest payment = Annual interest payment ÷ 2
= $390,000 ÷ 2 = $195,000
Step 3: Calculate the interest expense for the first 6 months (January 1, 2010, to June 30, 2010):
Interest expense = Carrying value of bonds on January 1, 2010 × Effective interest rate for the period
Carrying value of bonds on January 1, 2010 = Proceeds from bonds = $4,901,036
Effective interest rate for the period = Semiannual yield to maturity = 4%
Interest expense for the first 6 months = $4,901,036 × 4% = $196,041
Step 4: Calculate the interest expense for the last 6 months (July 1, 2010, to December 31, 2010):
Interest expense = Carrying value of bonds on July 1, 2010 × Effective interest rate for the period
Carrying value of bonds on July 1, 2010 = Carrying value of bonds on January 1, 2010 + Interest expense for the first 6 months - Semiannual interest payment
= $4,901,036 + $196,041 - $195,000 = $4,902,077
Effective interest rate for the period = Semiannual yield to maturity = 4%
Interest expense for the last 6 months = $4,902,077 × 4% = $196,083
Step 5: Add the interest expense for the first 6 months and the interest expense for the last 6 months to get the total interest expense for 2010:
Total interest expense for 2010 = Interest expense for the first 6 months + Interest expense for the last 6 months
= $196,041 + $196,083 = $392,124

A Company Issues $5,000,000, 7