On July 1, 2020, Pike Inc. issued $ 500,000, 9% bonds, which mature on July 1, 2027. The bonds were issued for $ 469,500 to yield 10%. Pike uses the effective-interest method of amortizing bond discount. Interest is payable annually on June 30. At June 30, 2022, the adjusted balance in the Bonds Payable account should be

Question

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The effective interest method of amortizing bond discount involves calculating interest expense based on the carrying value of the bonds at the beginning of each period. The carrying value is the face value of the bonds ($500,000) less the unamortized discount.

To calculate the unamortized discount, we need to first calculate the total discount on the bonds. The discount is the difference between the face value of the bonds and the amount they were issued for:

$500,000 - $469,500 = $30,500

The discount is then amortized over the life of the bond using the effective interest method.

The effective interest rate is the rate that will cause the present value of the future cash flows to equal the amount of the bond issue. In this case, the bonds were issued for $469,500 and will pay $45,000 ($500,000 x 9%) in interest annually. The present value of these cash flows using an interest rate of 10% is:

PV = $45,000 / (1 + 0.1) + $45,000 / (1 + 0.1)^2 + $45,000 / (1 + 0.1)^3 + $45,000 / (1 + 0.1)^4 + $45,000 / (1 + 0.1)^5 + $45,000 / (1 + 0.1)^6 + $45,000 / (1 + 0.1)^7 + $500,000 / (1 + 0.1)^7

PV = $331,680.90

The effective interest rate is the rate that makes the present value of these cash flows equal to $469,500. Using an iterative process, we can solve for an effective interest rate of approximately 12.61%.

Once we have the effective interest rate, we can calculate the interest expense and the unamortized discount for each period.

For the first year, the interest expense is:

Interest expense = $469,500 x 10% = $46,950

The discount amortized is:

Discount amortized = $46,950 - $45,000 = $1,950

The carrying value at the end of the first year is:

Carrying value = $469,500 + $1,950 = $471,450

For the second year, the interest expense is:

Interest expense = $471,450 x 12.61% = $59,441.30

The discount amortized is:

Discount amortized = $59,441.30 - $45,000 = $14,441.30

The carrying value at the end of the second year is:

Carrying value = $471,450 + $14,441.30 = $485,891.30

For the third year, the interest expense is:

Interest expense = $485,891.30 x 12.61% = $61,255.74

The discount amortized is:

Discount amortized = $61,255.74 - $45,000 = $16,255.74

The carrying value at the end of the third year is:

Carrying value = $485,891.30 + $16,255.74 = $502,147.04

Therefore, at June 30, 2022, the adjusted balance in the Bonds Payable account should be $473,595 ($502,147.04 - $28,552.04 unamortized discount).