You have a mortgage on your existing home. The mortgage payments are $2,046.73 per month (Note: this amount covers principal and interest only, and ignores property taxes and insurance payments.) You have lived in the house for 5 years, and the original mortgage was a 30-year fixed rate mortgage. The interest rate on the mortgage is 3.25% per year, compounded monthly. The next mortgage payment is one month away.

a. What is the effective annual interest rate on the mortgage?

b. What is the balance outstanding on the mortgage?

c. Interest rates have declined, so that you can take out a new mortgage at 2.875% per year, compounded monthly. You do not wish to extend the maturity of your mortgage; any new mortgage would have a maturity of 25 years. What is the new monthly payment on such a mortgage?

d.  What is the value of the savings today, if you switch to the new mortgage?