On January $1,2023,$ MTS Corporation issued a series of $100$ convertible bonds, maturing in $5$ years. The face amount of each bond was

$$500.$ MTS received $$50,800$ for the bond issue. The bonds paid interest every December $31$ at $5\%$; the market interest rate for bonds

with a comparable level of risk was $5\mathrm{.}50\%.$ The bonds were convertible to common shares at a rate of $10$ 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 into

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 $$30,380$ due to a decrease in market interest rates, a conversion inducement

of $$\frac{27}{?}$ bond was offered to the remaining bondholders to convert their bonds to common shares. All of the remaining $60$ bonds were

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 $1,2025.$