How to Manually Calculate a Mortgage

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Manually 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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