Anna is buying a house selling for $225,000.$ To obtain the mortgage, Anna is required to make a $10\%$ down payment. Anna obtains a $25-$year mortgage with an interest rate of $6\%$

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.

$PMT=\frac{L(\frac{r}{n})}{1-(1+\frac{r}{n}{)}^{-nt}}$

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.

$ $($Round to the nearest cent.$)$