On January $1,2023,$ MTS Corporation issued a series of $100$ convertible bonds, maturing in $5$ years. The face amount of each bond $$500.$ MTS received $$51,000$ for the bond issue. The bonds paid interest every December $31$ at $5\%$; the market interest rate for bo with a comparable level of risk was $5\mathrm{.}50\%.$ The bonds were convertible to common shares at a rate of $12$ common shares per bond. MTS amortized bond premiums and discounts using the effective interest method, and the company's year$-$end was December $31.$ MTS follows ASPE.

On January $1,2024,20$ of the bonds were converted into common shares. On June $30,2024,$ another $20$ bonds were converted int common shares. The bondholders chose to forfeit the accrued interest on these bonds.

On January $1,2025,$ when the fair value of the bonds was $$30,500$ due to a decrease in market interest rates, a conversion inducem of $$28/$bond was offered to the remaining bondholders to convert their bonds to common shares. All of the remaining $60$ bonds wer converted into common shares at this time.

a$.$ Prepare the journal entry at January $1,2023.$

b$.$ Prepare the journal entry at December $31,2023.$

c$.$ Prepare the journal entry at January $1,2024.$

d$.$ Prepare the journal entry at June $30,2024.$

e$.$ Prepare the journal entry at December $31,2024.$

f$.$ Prepare the journal entry at January $1,2025.$