Anna is buying a house selling for $$$$205$ comma $000205,000.$ To obtain the$$ mortgage, Anna is required to make a $2020\%$ down payment. Anna obtains a $2525-$year mortgage with an interest rate of $66\%.$

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$$a$)$ Determine the amount of the required down payment.

$$b$)$ Determine the amount of the mortgage.

$$c$)$ Determine the monthly payment for principal and interest.