Everyday Math

Math and the Consumer’s Money

What mathematical concept is used to calculate mortgage payments?

In most cases, a mortgage is based on amortization, which is the gradual elimination of a liability (a financial obligation or debt, such as a mortgage) in regular, fixed, systematic payments (such as monthly) over a specific period of time. These payments must be enough to cover both the principal borrowed and the interest. Although it is usually written in a complex set of mathematical calculations, simply put amortization means a part of the payment goes toward the interest cost and the remainder goes toward the principal (or the amount borrowed). The interest is then recomputed on the amount owed, and therefore it gets smaller and smaller as the ending balance of the loan becomes less and less. That is why the homeowner pays a great deal toward interest and not the principal for the first several years of a home mortgage.

For example, if a mortgage is taken out for $100,000 at 6.5 percent for 30 years, the fixed monthly principal and interest payment is $632.07. For the first month, the homeowner pays interest on the $100,000 (or $541.67), with the remainder of the payment ($90.40) going toward principal. In other words, the debt on the principal is reduced by $90.40. By the next month, the homeowner owes interest on a lesser amount of money—on $99,909.60 (or $100,000 - $90.40), not the $100,000, with $541.18 going toward interest and $90.89 going toward principal. As payments are made month after month, the interest decreases and the principal reduction increases. By the 360th payment (or 30 years later), the payment contributes $3.41 to interest and $628.66 to principal.


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