How to Calculate the Interest Paid on a Mortgage

Home buyers should consider mortgage terms when buying a home

When a person takes out a mortgage on a home, the lender will usually give the borrower an amortization table for the loan. The amortization table shows the amount of principal and the amount of interest contained in each monthly payment, as well as the remaining balance on the loan. The easiest way to calculate the interest paid on a mortgage is to add all the interest values from the amortization table up to the current payment period. If you do not have an amortization table, you can make one of your own.

Things You'll Need

• Calculator

Instructions

1. Determine your period interest rate (c) by dividing the annual percentage rate for your mortgage by the total number of payments per year. If you are on a monthly payment plan, you will divide by 12, but if you are on a biweekly payment plan, you will divide by 26.

   Example:
   APR = 6% (monthly plan)
   c = 0.06/12 = 0.005 or 0.5%

2. Determine the number of payments (n) due over the life of the mortgage. For long-term loans like mortgages, lenders usually give the term in years. Multiply the loan term in years by the total number of payments per year.

   30-year mortgage (monthly plan)
   n = 30 *12 = 360

3. Calculate the monthly or biweekly payment (P) due for the loan. You will need the original loan amount (L) for the calculation. The equation is:

   P = L[c(1 + c)^n]/[(1 + c)^n - 1]

   Example:
   $200,00 30-year fixed mortgage, paid monthly, at 6% APR
   L = $200,00
   n = 360
   c = 0.005

   P = 200000[0.005(1 + 0.005)^360]/[(1 + 0.005)^360 - 1]
   P = 200000[0.005*6.022575]/[6.022575 - 1]
   P = 200000 * (0.03011 / 5.022575)
   P = 1199.10

4. Calculate the amount of interest paid in the first payment by multiplying the loan amount by the period interest rate.

   200000 * 0.005 = $1000 interest

5. Calculate the amount of principal in the first payment by subtracting the interest amount from the payment amount and subtract that amount from the current loan value to obtain the new loan value.

   1199.10 - 1000 = $190.10 principal
   200000 - 190.10 = $199809.90 new loan value

6. Calculate the interest included in the second payment by multiplying the new loan value by the period interest rate. Calculate the principal and new loan value as before. Continue this process until the loan value reaches zero. This is your amortization table.

7. Add the interest values in the amortization table to obtain the total interest on the mortgage.

Tips & Warnings

• You can use this method for adjustable mortgages, but it is difficult to keep track of the values. Use the new interest rate when the mortgage adjusts to calculate a new payment value and a new period percentage rate. Use these new numbers only from the time the adjustment is made until another adjustment is made or the loan is paid in full.

References

• The Mortgage Professor: Mortgage Formulas

Resources

• The Mortgage Professor: Information for buyers and sellers