A $$$$90,000$ mortgage is to be amortized by making monthly payments for $25$ years. Interest is $5\mathrm{.}3\%$ compounded semi$-$annually for a seven$-$year term.

$($a$)$

Compute the size of the monthly payment.

$($b$)$

Determine the balance at the end of the seven$-$year term.

$($c$)$

If the mortgage is renewed for a seven$-$year term at $6\%$ compounded semi$-$annually, what is the size of the monthly payment for the renewal$$ term?

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Part $1$

$($a$)$ The size of the monthly payment is $$$$538\mathrm{.}92$

$($Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as$$ needed.$)$

Part $2$

$($b$)$ The balance at the end of the seven$-$year term is $$$$75,248\mathrm{.}1975$

$($Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as$$ needed.$)$

Part $3$

$($c$)$ The size of the monthly payment for the renewal term is $$$$567\mathrm{.}39$