On June $30,2024,$ the Jackson Co$.$ issued $$10$ million of its $8\%$ bonds for $$9\mathrm{.}2$ million.

The bonds were priced to yield $10\%.$

The bonds are dated June $30,2024$ and mature on June $30,2032.$ Interest is payable semiannually on December $31$ and July $1.$

If the effective interest method is used, by how much should the bond discount be reduced for the six months ended December $31,2024?$