Consider a $$500$ million pass$-$through backed by FRMs with a WAC rate of $5\mathrm{.}5\%,$ pass$-$through rate of $4\mathrm{.}75\%$ and WAM of $356$ months.

a$.(3$ points$)$ What is the interest amount the pass$-$through will pay in month $1?$

b$.(6$ points$)$ What is the scheduled principal payment in Month $1$ by the pass$-$through?

c$.(6$ points$)$ Assuming $150$ PSA, what is the SMM in Month $1$ for the pass$-$through?

$5.(3$ points$)$ A floater and an inverse floater are being created from a CMO tranche with a par value of $$150,000$ and a coupon rate of $4\mathrm{.}5\%.$ If the coupon rate of the floater is LIBOR $+0\mathrm{.}5\%$ and the coupon leverage is $3,$ then the coupon rate of the inverse floater will be $\_$K$\_\_-3\backslash$times LIBOR. What is K$?$