What Are the Mathematics Behind a Mortgage Loan Calculator?

Mortgage calculators use loan amount, interest rate and number of monthly payments to compute the amount of a monthly mortgage payment, according to Interactive Mathematics. Many websites offer interactive mortgage calculators to perform this calculation, but the math can be performed at home without using an interactive calculator.

To calculate payment amount, the loan amount (L) is multiplied by the interest rate (R) and then that result is divided by the result of one minus (the rate plus one) to the negative power equal to the number of payments (N), says Interactive Mathematics. For a 30-year mortgage, the number of payments is 360, or 12 times 30. To calculate a monthly amount, the annual interest rate has to be divided by 12, meaning a 6 percent interest rate is expressed as 0.005 instead of 0.06. Mathematically, order of operations dictates that expressions within parenthesis (the rate plus one) are calculated first and are followed by exponential calculations (to the negative power of the number of payments), then multiplication and division.

Interactive mortgage calculators available on websites such as MortgageCalculator.org, BankRate.com and Zillow.com can automatically include monthly costs other than mortgage principal and interest like homeowners insurance, property taxes and mortgage insurance. These calculators perform the math for potential home buyers and remove the potential for user math errors in computing amounts.