Eight years ago the Matthew family made a down payment on a house of $20\%$ of the purchase price and

secured a bank loan of $$314,000$ to finance the remaining amount. The terms of the $25-$year mortgage include an interest

rate of $6\mathrm{.}5\%$ per year, compounded monthly.

$($a$)$ Interest rates have dropped to $3\mathrm{.}25\%$ per year, compounded monthly, on a $15$ year mortgage. The Matthews are

thinking about refinancing. If they refinance, what will their new monthly payments be$?$

$($b$)$ How much will the Matthews save by refinancing?

Thank you for the help!