A loan of $$490,000$ is amortized with payments at the end of each month and an interest rate of $9\mathrm{.}9\%,$ compounded monthly.

Use Excel to create an amortization table showing each payment and the corresponding beginning blance, interest owed, payment amount, principal, and ending balance. Answer the following, rounding to the nearest penny.

Suppose the mortgage is paid off over $30$ years.

a$)$ Find the amount of each payment. $

b$)$ Find the total of all payments made over the life of the loan. $

c$)$ Find the total amount of interest paid over the life of the loan. $

Suppose that the mortgage is amortized over $15$ years instead of $30$ years.

d$)$ Find the amount of the new payment. $

e$)$ Find the dollar amount by which the monthly payment increased as compared to the $30-$year amortization. $

per month

f$)$ Find the total amount of interest paid over the life of the $15-$year loan. $

g$)$ Compare the answer from part c$)$ and f$)$ above to find the total amount of interest saved by amortizing over $15$ years instead of $30$ years.

$