On January $2,2024,$ West Co$.$ issued $9\%$ bonds in the amount of $$500,000,$ which mature on January $2,2034.$ The bonds were issued for $$414,000$ to yield $12\%.$ Interest is payable semiannually on June $30$ and December $31.$ West uses the effective interest method of amortizing bond discount. In its June $30,2024$ balance sheet, what amount should West report as bonds payable, net of remaining discount?

a$.$ $$414,000$

b$.$ $$416,340$

c$.$ $$417,870$

d$.$ $$418,680$