# How to Manually Calculate a Mortgage

by Contributing Writer ; Updated July 27, 2017Manually calculating the monthly payments on a given loan is fairly simple, but it does require some basic algebra skills—or access to the Internet. The formula to calculate a mortgage is M = P [(R/12)(1 + (R/12))^n ] / [ (1 + (R/12))^n - 1], where M = the monthly payment, P = the principal on the loan, R = the annual interest rate, and n = the number of months to pay off loan.

Divide your annual interest rate (R) by 12 and write it down. This is, essentially, your monthly interest rate, which we’ll refer to in the following steps as r.

R/12 = r

Add 1 to r and take that new number to the power of n, where n equals the number of months on your loan. For example, if your loan is for 30 years, then n equals 360. This step will require a calculator with a y^x function, or the manual calculation of (1+r) times itself n times. We’ll call this new number x.

(1+r)^n = x

Multiply x by r. Divide this new number by x minus 1. We'll call this number y.

(x)(r) / (x-1)

Multiply y by the loan principal (P). The resulting number is the monthly mortgage payment (principal and interest) on the loan.

(y)(P) = Monthly Payment

Numerous websites have free mortgage calculators. You can find a link to some in the Resources section. Simply input the interest rate, the duration, and the amount of your loan, and the websites will do the rest.

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