Txtiles, an online clothing manufacturer, has $$100,000$ of $7\%$ bonds at $96$ when the market rate is $8\%,$ and they pay interest semiannually at $6/30$ and $12/31.$ The bonds are dated January $1,2017,$ and they are issued on April $1,2017.$ How much cash will Txtiles collect at issuance of the bond?

a$.$ $$100,000$

b$.$ $$96,000$

c$.$ $$97,750$

d$.$ $$101,750$