On January 1, a company issued 9%, 10-year bonds with a face amount of $90 million for $84,392,051 to yield 10%. Interest is paid semiannually. What was interest expense at the effective interest rate on June 30, the first interest date? (Enter your answers in whole dollars. Round percentage answers to 1 decimal place (e.g., 0.0234 should be entered as 2.3).)
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To calculate the interest expense using the effective interest rate method, we'll first determine the semiannual interest payment based on the bond's face value and coupon rate.
Given:
Face amount of bonds = $90,000,000
Issue price of bonds = $84,392,051
Coupon rate = 9% (per annum)
Number of periods = 10 years
Interest payment frequency = semiannual
First, let's calculate the semiannual interest payment:
Semiannual interest payment = Face value × Coupon rateb / Number of payments per year
Semiannual interest payment = $90,000,000×9% / 2
Semiannual interest payment = $90,000,000×0.09 / 2
Semiannual interest payment = $4,050,000
Now, we'll calculate the interest expense on June 30, the first interest date, using the effective interest rate method.
The effective interest rate is the rate at which the bond's present value equals the issue price.
Effective interest rate = Interest payment / Issue Price x Number of periods per year
Effective interest rate = $4,050,000 /$84,392,051 x 2
Effective interest rate = 0.048×2
Effective interest rate = 9.6%
The interest expense on June 30 is based on the carrying amount of the bond multiplied by the effective interest rate:
Interest expense = Carrying amount of bond × Effective interest rate
The carrying amount of the bond is the issue price on January 1.
Interest expense = $84,392,051 × 9.6%
Interest expense = $8,093,282
Therefore, the interest expense at the effective interest rate on June 30, the first interest date, is approximately $8,093,282.