An investor owns a $$10$ million par value of a $7\mathrm{.}85\%,5-$year bond of a BBB rated corpo$-$ ration, purchased at par value. The coupon payments are semiannual. At the same time, the investor enters into a $5-$year interest$-$rate swap with a dealer, where the investor pays a fixed rate and receives $6-$month LIBOR. Assume the fixed swap rate is $7\mathrm{.}00\%.$

answer the following:

$($a$)$ What is the net payment received by the investor every six months, assuming the issuer does not default and there is no change in the $6-$month LIBOR?

$($b$)$ If the swap rate in the market changes to $7\mathrm{.}30\%$ instead of $7\mathrm{.}00\%,$ and the investor sells the bond to the dealer at par value entering an asset swap agreement to pay semiannually at $7\mathrm{.}30\%$ and receive $6-$month LIBOR plus $30$ basis points, what would be the net payment received by the investor every six months?