Guadalupe is buying a home for $$451,000$ and has come to your bank for a mortgage. Your bank requires a $13\%$ down payment and charges $2\mathrm{.}5$ points for the loan. She is seeking a $25$ year mortgage and your bank can offer her a $3\mathrm{.}05\%$ conventional loan.

Round all currency answers to the nearest cent.

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

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b$)$ Determine the amount of the loan.

$ $$ I

c$)$ Determine the amount Ingrid will have to pay for points. Remember, points are pre$-$paid interest and are not included in the loan amount. Hint: One point equals $1\%$ of the loan amount.

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d$)$ In order to determine the amount of the monthly payment, which formula is appropriate?