Question $4($Mortgage$-$backed securities$)(20$ marks$)$ This question has two independent parts, $($a$)$ and $($b$).($a$)$ A $\backslash (\backslash$$ $10000\backslash )$ mortgage passthrough security has a passthrough rate of $\backslash (4\mathrm{.}5\backslash \%\backslash ),$ a WAC of $\backslash (4\mathrm{.}92\backslash \%\backslash ),$ a WAM of $8$ months, and an original maturity of $30$ years. A $\backslash (4\mathrm{.}5\backslash \%\backslash )$ coupon rate PAC tranche $(\backslash (70\backslash \%\backslash )$ of the passthrough par value$)$ and a $\backslash (4\mathrm{.}5\backslash \%\backslash )$ coupon rate support tranche $(\backslash (30\backslash \%\backslash )$ of the passthrough par value$)$ are created out of this passthrough. The initial PAC collar is $\backslash (90-200\backslash )$ PSA. Suppose the actual prepayment rate is $250$ PSA. Calculate the net interest and principal payments to the PAC and support tranches in Month $1.(10$ marks$)($b$)$ Consider a $\backslash (\backslash$$ $25,000\backslash )$ passthrough with a WAC of $\backslash (6\backslash \%\backslash )$ and a WAM of $354$ months. Given the prepayment speeds assumed in the following table, compute, for each month in the table: SMM$,$ CPR$,$ outstanding balance, mortgage payment, interest, scheduled principal repayment, prepayment, total principal, and total cash flow. Please show your calculations and do not use Excel. $(10$ marks$)$