On January 1, 2020, Gottlieb Corporation issued $4,000,000 of 10-year, 8% convertible debentures at 102. Interest is to be paid semiannually on June 30 and December 31. Each $1,000 debenture can be converted into eight shares of Gottlieb Corporation $100 par value common stock after December 31, 2021.

On January 1, 2022, $400,000 of debentures are converted into common stock, which is then selling at $110. An additional $400,000 of debentures are converted on March 31, 2022. The market price of the common stock is then $115. Accrued interest at March 31 will be paid on the next interest date.

Bond premium is amortized on a straight-line basis.

Make the necessary journal entries for:

a. December 31, 2021.

b. January 1, 2022.

c. March 31, 2022.

d. June 30, 2022.

I understand a and b. I know c is:

Interest expense 7800

Premium on Bonds Payable 200

Interest Payable 8,000

Bonds Payable 400,000

Premium on Bonds Payable 6200

Common Stock 320,000

Paid-in Capital in Excess of Par 86,200

However, I do not understand how to get the premium on bonds payable and interest expense numbers for the first entry made on March 31, 2022. For the premium on bonds payable the calculation was shown to be [(6400/8) * (3/12)], and for the interest expense the calculation was shown to be [400,000 * 0.08 * (3/12)], but I do not understand why these numbers are used to calculate those parts. I know premium on bonds payable is debited for $6400 on January 1, 2022, but do not understand why the 6400 is involved for the first entry on March 31, 2022. Please explain why or please shown another way to get the same answer that might be more understandable as to why certain numbers are being used and where these numbers come from.