$1.$ Consider a $$4\mathrm{.}4$ million loan that is used to finance the acquisition of an apartment building. The loan has a $3\mathrm{.}15\%$ interest rate and will be amortized over $30$ years. The term to maturity is $5$ years. a$)$ What is the mortgage$$s monthly debt service? b$)$ What is the mortgage$$s annual debt service? c$)$ How much principal does the borrower pay in Month $6?$ d$)$ How much interest does the borrower need to pay in Month $9?$ e$)$ How much principal will the borrower repay during Year $3?$ f$)$ How much interest will the borrower pay in the Year $4?$ g$)$ What is the outstanding loan balance at the end of Month $4?$ h$)$ What is the outstanding loan balance at the end of Month $32?$ i$)$ What is the loan$$s balloon payment?