# How is a Mortgage Payment Calculated?

## Payments

Mortgage payments are calculated with an algebraic formula that takes into account the term of the loan, the interest rate and the amount of the loan. The formula ensures that the same payment is made each month of the term, even though the amount of principal and interest are varying. This process is called amortization.

## Variables

The formula used to calculate the value of the monthly payment includes three variables. The first is the total number of payments. Most of the time, payments will be made monthly, but bimonthly and biweekly payments are also possible. The interest rate used is the interest rate for the period in between payments and is obtained by dividing the APR by the number of payments in a year. The final variable is the total amount of the loan.

## The Formula

The formula used to calculate payment value is P = V[n(1 + n)^t]/[(1 + n)^t - 1] P = monthly payment t = total number of payments n = monthly interest V = loan amount This formula is a bit complex, so it helps to break it down into parts to solve it. If you have a computer with a spreadsheet program, it probably has this formula already programmed. For Microsoft Excel, the function for this calculation is called "PMT."

## Solving the Equation

To solve the equation, you need to work from the inside out. In this example, there is a 30-year fixed rate mortgage, which equates to 360 total monthly payments (t). The annual percentage rate is 6.0%, which, when divided by 12, reduces to 0.005 monthly interest rate (n). The total value of the loan is \$200,000 (V). Calculate (1+n)^t; 1+n = 1.005; (1+n)^t = 6.023 Calculate the numerator inside the brackets; t(6.023) = 0.03 Calculate the denominator inside the brackets; 6.023-1 = 5.023 Calculate the fraction; 0.03/5.023 = 0.006 Calculate the payment; 200,000*0.006 = 1199.08