1) When you take out a mortgage loan to buy a house, the payments are computed based on the amortization period. If the amortization period is 25 years, the monthly payments are computed as the amount you would have to pay every month to pay off the loan in exactly 25 years.

Assume the mortgage is for $500,000. Let the nominal annual interest rate be 6%.

a) What is the monthly payment X for this mortage?

Even though the amortization period is 25 years, a typical mortgage is only for 5 years (and then the homeowner has to pay off the outstanding balance, usually by getting a new mortgage.

b) How much does the homeowner still owe at the end of the 5 year mortgage?

c) If the homeowner enters a new mortgage for the outstanding balance after 5 years, and the interest rates are exactly the same, what is the monthly payment on the new mortgage? Why is it different from the answer to a) ?