On January $1,2023,$MTS Corporation issued a series of $100$convertible bonds, maturing in $5$years$.$ The face amount of each bond was $$500.$MTS received $$51,000$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 $12$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 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 $$30,500$due to a decrease in market interest rates, a conversion inducement of $$28/$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. $1)$ Prepare journal entry at January $1,2023.2)$ Prepare journal entry at Dec $31,2023.3)$ Prepare journal entry at Jan $1$st $2024$ and June $30,2024.4)$Prepare journal entry at Dec $31,2024.5)$ Prepare journal entry at Jan $1,2025.$