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When markets are working smoothly, exchanges should be equal. In a mortgage setting, the cash
loaned now should be equal to the present value of the repayments. We have a relationship like this:
$200,000 = PV of repayments
Payments should cover interest and any payment above interest is a reduction of principal.
I’ll show an example of the repayment schedule for a four year loan for $100,000 at 8 percent. Find the
payment as
$100,000 = payments * 3.312
Each year’s payment of $30,192 will cover the interest on the loan balance and the remainder of the
payment reduces the principal. An amortization schedule would look like this:
year payment interest repay
principal Loan balance
100,000
1 30,192 8,000 22,192 77,808
2 30,192 6,225 23,967 53,840
3 30,192 4,307 25,885 27,956
4 30,192 2,236 27,956 0
Problem Statement
House Mortgage
You have just purchased a house and have obtained a 30-year, $200,000 mortgage with an interest rate
of 10 percent. Let’s say that you make a single annual payment at the end of each year.
Required:
1. What is your annual payment?
2. Assuming you bought the house on January 1, what is the prinicipal balance after 1 year?
3. After four years, mortgage rates drop to 8 percent for 30-year fixed-rate mortgages. You still have the
old 10 percent mortgage you signed four years ago and you plan to live in the house for another five
years. The total cost to refinance the mortgage is $3,000, including legal fees, closing costs, and points.
The rate on a five-year CD is 6 percent. Should you refinance your mortgage or invest the $3,000 in a
CD? The 6 percent CD rate is your opportunity cost of capital.
