$(6-$point$)$ Pam and Tom just got a $7\mathrm{.}75\%,30-$year mortgage

for $$500,000.1)$ How much is their monthly payment for

principal and interest? $2)$ How much interest will they pay

on this mortgage in the first year? $3)$ How much principal

will they pay the first year?

$(8-$point$)$ Five years later Pam and Tom noticed that

interest rates for comparable mortgages have fallen to

$4\mathrm{.}75\%.$ Assuming Pam and Tom have made all their

payments on time, $1)$ what is the outstanding mortgage

balance that could be refinanced after $60$ payments?

Assuming they could get a $4\mathrm{.}75\%,30-$year mortgage, $2)$

what would their new monthly payment be$?3)$ What

would their new payment be if they chose a $25-$year

mortgage? $4)$ A $15-$year mortgage?