(This problem is designed to illustrate the potential savings from paying a mortgage off faster. It may be viewed as an illustration of an assured, risk-free return, except that the return is the interest you save instead of interest you earn.)

You have a 20-year $100,000 mortgage with a 9 percent interest rate. (To reduce the size of this problem, assume that payments are made annually and not monthly as would be the normal case with a mortgage.)

a) Determine the repayment schedule.

b) How much is owed after ten years?

c) How much will be the total payments made over the 20 years?

d) How much interest is paid over the 20 years?

e) If you increase your first-year payment to include the next year’s principal payment, how much interest will you pay at the end of the second year?

f) If each year your payment includes the current required payment and the subsequent year’s principal repayment, what will be the life of the mortgage?
g) If you follow the process in (f), what are the total payments and the interest payments made over the life of the mortgage?
h) What are the advantages and disadvantages associated with this early payment strategy?
i) If interest rates decline to 7 percent, what is the current value of the mortgage based on the assumption that the loan will be outstanding for 20 years? (That is, if you were buying this mortgage as an investment for a mortgage pool, how much would you be willing to pay?)
j) If interest rates decline to 7 percent and you follow the strategy in (f), what is the current value of the mortgage?
k) If interest rates decline to 7 percent and you expect to refinance after four years (i.e., repay the loan with no prepayment penalty), what is the current value of the mortgage?
l) Why do your valuations in (i) through (k) differ?