Calculating Home Mortgage Interest

The biggest loan in most individuals' financial lives is a home mortgage. In contrast to a short-term auto loan, a home mortgage loan can run out to 30 years, and the amount borrowed is usually much larger than for an automobile.

Suppose that you recently bought the home of your dreams and qualified for a $250,000 mortgage loan for 30 years at a 6 percent annual interest rate. The loan requires monthly payments, so you divide the annual interest rate by 12 to determine the monthly rate, which is 0.5 percent (or 1/2 of 1 percent) per month. In almost all cases the monthly payments over the life of a mortgage loan are equal and uniform. Assuming uniform payments over the 30-year life of the loan, how much would each of your 360 loan payments be? How do you determine this amount? You probably would assume that the lender's quoted amount is correct — and you'd be pretty safe in this assumption. But how can you be sure?

You can use a relatively inexpensive business/financial calculator to quickly determine monthly loan payments. These handy tools have special keys for entering each of the variables of a loan. To determine the monthly payment in this example, pull out your trusty calculator and enter the following numbers for each variable:

N = number of periods — 360 months in this example
INT = interest rate per period — 0.5 percent per month in this example. (These calculators assume that interest is a percentage, so type .5, not .005.)
PV = present value, or amount borrowed today (the present time) — $250,000 in this example
FV = future value, or principal amount owed after the final monthly loan payment is made — $0 in this example. (This means that the loan is fully paid off after the last monthly loan payment; otherwise, you enter the amount of the balloon payment due at the end of the loan.)
PMT = payment per period based on the four numbers just entered — $1,498.88 in this example. (This is the amount you solve for, which appears as a negative number, meaning that you have to pay this amount per month.)
The big advantage of using a business/financial calculator is that you can enter the known numbers (the first four) and then simply hit the button for the unknown number, which appears instantly. Another big advantage is that you can keep these numbers in the calculator and make "what if" changes very quickly. For example, what if the annual interest rate were 4.8 percent? Just reenter the new interest rate (0.4 percent per month) and then call up the new monthly payment amount, which is $1,311.66. The monthly payment difference times 360 payments is $67,396.65 less interest over the life of the loan. It definitely pays to shop around for a lower rate.

If you use the Internet, you can find many Web sites that provide online financial calculators. You can go to one of the popular Web search engines, such as Yahoo or Google, and type "financial calculator" in the search bar. From the list you get, select one that seems to fit your needs. Also, Microsoft Excel and other spreadsheet programs include a financial function for calculating the monthly payment for a mortgage. The old-fashioned method — before handheld calculators and personal computers came along — was to use printed tables that give the factors for different interest rates and time periods per $1,000. Surprisingly, many people still use these tables, and accounting and finance textbooks still include them. Old habits die hard.

Each mortgage payment is divided between interest for the month and principal amortization, which refers to the reduction of the loan balance. For the first month of our example, the interest amount is $1,250 ($250,000 loan balance x 0.5 percent monthly interest rate = $1,250). Therefore, the first month's principal reduction is only $248.88. Right off, you can see that the loan's principal balance will go down slowly — and that a 30-year mortgage loan involves a lot of interest. Lenders provide you with a loan payoff (amortization) schedule. Take a look, although trying to follow down a table of 360 rows of monthly payments is tedious.