A mortgage is a loan taken out for the purchase or construction of a home. Most mortgages are amortised over the term of the loan with a set monthly payment for the entire loan. However, the amount of each monthly payment that goes to interest versus principal varies. At the start of the loan, most of the monthly payment goes to interest payments. To calculate how much you owe on your mortgage, you need to know how much you borrowed, the interest rate, the monthly payment and how many payments you have made to date.

Convert the annual interest rate as a percentage to a monthly interest rate expressed as a decimal by dividing by 1,200 and call the result "R." For example, if your annual interest rate is 6.03 per cent, divide 6.03 by 1,200 to get 0.005025.

Check your financial records to determine the total amount you borrowed, the amount of your monthly payment and the number of monthly payments you have made. Call the amount borrowed "B," the monthly payment amount "M" and the number of monthly payments already made "P."

Use the formula B_(1+R)^P -- M/R_((1+R)^P-1) to calculate the principal remaining on your mortgage payment. The following steps break this down into smaller, more manageable steps.

Plug in B, R and P into the expression B_(1+R)^P. For example, if you borrowed £216,450, had an interest rate of 0.061 and wanted to know how much you owed after 60 payments, you would plug in 333,000_(1+0.005025)^60 to get £292,394.60. .

Divide M by R. In this example, if you had a 30-year mortgage your monthly payment would be £1,301.90, so you would divide £1,301.90 by 0.005025 to get £259,085.40.

Plug in R and P into (1+R)^P-1. In this example, you would get (1+0.005025)^60-1, which is equal to 0.35086484.

Multiply the result from step 5 by step 6. Continuing the example, you would multiply £259,085.40 by 0.35086484 to get £90,903.90.

Subtract the result from step 7 from the result from step 4 to find the outstanding balance on your mortgage. Finishing the example, you would subtract £90,903.90 from £292,394.60 to find you have £201,490.70 left on your mortgage.