$On$ January $1,2023,BDM$ Corporation issued a series $of100$ convertible bonds, maturing $in5$ years. The face amount $of$ each bond

was $$500.BDM$ received $$50,800$ for the bond issue. The bonds paid interest every December $31at4\%$; the market interest rate for

bonds with a comparable level $of$ risk was $4\mathrm{.}50\%.$ The bonds were convertible $to$ common shares $at$ a rate $of8$ common shares per

bond. $BDM$ amortized bond premiums and discounts using the effective interest method, and the company's year$-$end was December

$BDM$ follows ASPE.

$On$ January $1,2024,20of$ 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 $1,2025.$