A young couple buying their first home borrow $$70,000$ for $30$ years at $7\mathrm{.}5\%,$ compounded monthly, and make payments of $$489\mathrm{.}45.$ After $5$ years, they are able to make a one$-$time payment of $$2000$ along with their $60$th payment.

$($a$)$ Find the unpaid balance immediately after they pay the extra $$2000$ and their $60$th payment. $($Round your answer to the nearest cent.$)$

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Incorrect: Your answer is incorrect.

$($b$)$ How many regular payments of $$489\mathrm{.}45$ will amortize the unpaid balance from part $($a$)?($Round your answer to the nearest whole number.$)$

Incorrect: Your answer is incorrect.

payments

$($c$)$ How much will the couple save over the life of the loan by paying the extra $$2000?($Use your answer from part $($b$).$ Round your answer to the nearest cent.$)$

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