Mrs$.$ Barb E$.$ wants to purchase a new house for $$470,000.$ She has just enough savings for the $20\%$ down payment, which means that she will need a loan for the remaining amount. The mortgage will be a $30-$year loan with monthly payments and a $3\mathrm{.}375\%$ APR. Mrs$.$ Barb E$.$ would like to pay back the loan as soon as possible. She plans on paying $$400$ each month, in addition to the monthly payment, to reduce the principal.

a$)$ Find the monthly payment for the mortgage. Please enter the payment in cell C$22.$ The number should be formatted using $$Currency$$ with two decimals.

b$)$ Build an amortization table to calculate how many payments does she save with the additional $$400$ each month.

$$ Enter the amortization table in cells B$28$:H$389.$

$$ Utilize formulas, and not Excel functions, to find the Interest and Principal payments every period.

$$ The table must only include relative and absolute references.

$$ The formulas entered in period $1$ should be able to be copied down to the end of the table.

$$ Enter the number of periods saved in cell D$26.$