You have taken out a 30-year fixed-rate mortgage for $500,000.00 that requires you to make a fixed monthly payment every month for the next 360 months, with the first payment being made exactly one month from now.The stated interest rate is 4 percent, compounded monthly.

a.What are the monthly payments?

b. For the first payment, what is the amount of that payment that repays principle?

c.Right after you make the first monthly payment (i.e., essentially one month from now), using your answers to be above, what will be the remaining principle on the loan?

d.Right after you make your first payment, what is the present value of the remaining monthly paymentscompares to your answer to c above? Greater than, Equal to or Less than?

A. Greater than

B. Equal to

C. Less than

e.Using the result, you can infer from comparing c and d above, answer the following question.After you have made 180 monthly payments, what is the remaining principle?