How to Calculate Home Mortgage Interest

Solve for mortgage interest with any calculator that has an exponent key.

Any given mortgage payment has a portion that goes toward paying down the outstanding balance, a portion for paying interest that accumulated since the last payment and ancillary fees for taxes, insurance and the like. As you pay down the principal, the interest that accumulates between payment dates drops, so more of each payment can go toward paying off the principal. You can calculate the interest proportion of a given payment in a mortgage schedule by following a simple sequence of formulas.

Things You'll Need

• Calculator with an exponent key

Instructions

1. Calculate the periodic interest rate by dividing the nominal (stated) interest rate by 12 months. Denote the periodic rate with the letter i.

   As an example, if the nominal rate is 6 percent, the periodic rate is 0.5 percent.

2. Identify the total number of payments for the life of the loan. For a 30-year mortgage with monthly payments, this is 30*12 = 360. Denote the payment count with the letter T.

3. Count or identify the payment in the mortgage schedule for which you want to know the interest portion. Denote it with the letter N.

   For example, if you want to know the interest in the 10th payment, then N = 10.

4. Calculate (1+i)^(T-N+1), denoting it with the letter X. Here, the caret [^] indicates the start of the exponent or power of 1+i.

   For example, the 10th payment of a 360-payment mortgage with periodic interest rate 0.5 percent gives X = (1.005)^(360-10+1) = 5.758 after rounding.

5. Identify the payment amount for principal and interest combined, leaving out the fees for insurance, taxes and the like. Denote the periodic payment with the letter P.

6. Calculate the principal after the N-1-th payment with the formula (P/i)*(1-1/X). Denote it with the letter B, for "balance." Note that this is the balance that earns the interest during the month before the N-th payment is due.

   Continuing with the example from above, suppose the monthly payment is $2,000. Then B = (2000/0.005)*(1-1/5.758) = $330,531.43.

7. Solve for B*i to get the interest accumulated between the N-1-th and the N-th payment. This is the amount of interest paid by the Nth payment.

   Continuing from above, B*i = $330,531.43 * 0.005 = $1,652.66. So over 80% of the 10th payment goes toward paying interest.

References

• "The Theory of Interest"; Stephen Kellison; 1996
• Vertex 42: Amortization Calculation Formula
• Microsoft: IPMT Function
• Vertex 42: Amortization Formulas in Excel