When Gustavo and Serrana bought their home, they had a $5\mathrm{.}3\%$ loan with monthly payments of $$870\mathrm{.}60$ for $30$ years. After making $78$ monthly payments, they plan to refinance ror an amount that includes an additional $$35,000$ to remodel their kitchen. They can refinance at $4\mathrm{.}5\%$ compounded monthly for $25$ years with refinancing costs of $$625$ included with the amount refinanced.

$($a$)$ Find the amount refinanced. $($Round your answer to the nearest cent.$)$

$$

$($b$)$ Find their new monthly payment. $($Round your answer to the nearest cent.$)$

$ $$

$($c$)$ How lona will it take to pay off this new loan if they pay $$1200$ each month? $($Round your answer up to the next whole number.$)$

$$ payments

Need Help? $$