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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.
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.
P = V[n(1 + n)^t]/[(1 + n)^t - 1]
P = monthly payment
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).
This value only includes principal and interest on the loan. Most lenders require that property taxes and insurance premiums be paid with the mortgage payment. The annual insurance premium's property tax estimates are divided by 12 and added to the principal and interest values. This payment is commonly referred to as "PITI," or "principal, interest, tax and insurance," and represents the total mortgage payment.