A$$ variable$-$rate mortgage of $$$$116$ comma $000$ is amortized over $20$ years by equal monthly payments. After $18$ months the original interest rate of $7\%$ compounded semi dash annually was raised to $8\mathrm{.}8\%$ compounded semi dash annually. Three years after the mortgage was taken$$ out, it was renewed at the request of the mortgagor at a fixed rate of $7\mathrm{.}1\%$ compounded semi dash annually for a$$ four$-$year term.

$($a$)$ Calculate the mortgage balance after $18$ months.

$($b$)$ Compute the size of the new monthly payment at the $8\mathrm{.}8\%$ rate of interest.

$($c$)$ Determine the mortgage balance at the end of the$$ four$-$year term.

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Part $1$

$($a$)$ The mortgage balance is $$$

$$

enter your response here after $18$ months.

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

Part $2$

$($b$)$ The size of the new monthly payment is $$$

$$

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 mortgage balance is $$$

$$

enter your response here.