Designer Company issued $10-$year bonds on January $1.$ The $6\%$ bonds have a face value of $$800,000$ and pay interest every January $1$ and July $1.$ The bonds were sold for $$690,960$ based on the market interest rate of $8\%.$ Designer uses the effective interest rate method to amortize bond discounts and premiums. On July $1$ of the first year, Designer should record an interest expense $($rounded to the nearest dollar$)$ of

a$.$ $$24,000$

b$.$ $$27,638$

c$.$ $$48,000$

d$.$ $$55,277$