Q:

What Are Mortgage Equations, and How Are They Calculated?

A:

A mortgage equation is the mathematical formula that a lender uses in order to determine the borrower's fixed monthly payment to pay off a mortgage loan over a period of time. The lender calculates a mortgage amount using a variety of factors including the total purchase price of the property and the interest rate of the loan, explains Mortgage Professor.

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Although the mortgage equation for any given loan depends on the specific lender, most equations take the applicable interest rate and apply it to an exponential that equals the number of months in the loan. The lender then again multiplies the figure by the interest rate and divides it by another calculation of the interest rate. The lender then multiplies that figure exponentially by the term of the loan, minus one, says Nerd Wallet.

When using this formula, the lender must calculate the payments using the monthly interest rate rather than the annual interest rate. Using this equation, the longer the term of the loan, the less the borrower pays each month. However, a long loan means that the borrower pays more interest over the total life of the loan, explains Nerd Wallet. Another way to decrease monthly payments is to lower the principal on the loan. If the loan includes escrow payments, the amount of the loan might change each year because escrow payments often change over time.

The mathematical formula to calculate a mortgage payment also depends on whether the lender includes fees and points in the mortgage amount, explains Mortgage Professor. Some situations might result in a mortgage payment that changes over time, for example, if the borrower secures mortgage insurance. Interest rates are not necessarily fixed. A borrower might find a lower mortgage rate by shopping among lenders.