A $$$$88$ comma $000$ mortgage is to be repaid over a twenty$-$year period by monthly payments rounded up to the$$ next$-$higher $$100.$ Interest is $7\mathrm{.}5\%$ compounded semi dash annually.

$($a$)$

Determine the number of rounded payments required to repay the mortgage.

$($b$)$

Determine the size of the last payment.

$($c$)$

Calculate the amount of interest saved by rounding the payment up to the next higher$$ $$100$ versus rounding the payment to the nearest cent.

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Part $1$

$($a$)$ The number of rounded payments required to repay the mortgage is

$$

enter your response here.

$($Round up to the nearest whole$$ number.$)$

Part $2$

$($b$)$ The size of the last payment will be $$$

$$

enter your response here.

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

Part $3$

$($c$)$ The amount of interest saved is $$$

$$