The Yang family plans to buy a new house soon and is considering mortgage options. They are considering

two options, a $15-$year mortgage with an APR of $2\mathrm{.}75\%$ or a $30-$year mortgage with an APR of $3\mathrm{.}14\%.$ Both

options compound interest monthly. Currently the Yang family spends $($e$)$ $$\_\_\_1041\_\_\_\_\_\_\_$ each month in

rent and plan to spend the same amount on a mortgage payment. They do not currently have a down payment

and will finance the full price of the home. Round answers to whole numbers.

a$.$ If the Yang family chooses the $15-$year mortgage, how much will they be able to borrow? $(3$ pt$)$

b$.$ If the Yang family chooses the $30-$year mortgage, how much will they be able to borrow? $(3$ pt$)$

c$.$ Which option will allow the Yang family to borrow the most? By how much? Respond in a complete

sentence. $(3$ pt$)$

d$.$ Under which option will the Yang family spend the most overall? By how much? Respond in a complete

sentence. $(4$ pt