Are you able to do this problem through excel step by step: You have decided to purchase a house for $$400,000$ and are evaluating your options for the mortgage. Assume that your down payment will be $20\%$ of the purchase price, payments will be made monthly, and the first payment will be made one month from today.

What is the mortgage amount?

If you select the $30-$year mortgage, the interest rate will be $5\%$ annually. What is the monthly payment?

Suppose that the bank is also offering a $15-$year mortgage at $4\mathrm{.}625\%$ annually. What is the monthly payment on this mortgage?

What is the total of all payments for each mortgage? Which one costs you the least over the life of the mortgage?