How Does Interest Accrue on a Mortgage?

Interest is a fact of life on a mortgage. The bank lends you a substantial amount of money to buy a home, and it's not doing it as a favor. Charging you interest on the loan is one way the bank makes money on the transaction. Understanding how interest is calculated every month and accrued, or added to the principal, may influence the interest rate you accept when applying for a mortgage.

Monthly Accrual

Lenders typically calculate interest on a monthly basis, using the annual mortgage interest rate divided by 12. Consider a 30-year mortgage of $600,000 with an interest rate of 4.5 percent. Your monthly payment on that mortgage would be $3,040.00, which is the payment you must make to pay the monthly interest and reduce you principal every month all the way down to $0 after 30 years.

The interest in the first month would be calculated by taking the annual interest rate divided by 12 and applying it to the initial mortgage balance of $600,000. Taking 4.5 percent divided by 12 you get 0.375 percent per month. Multiplying it by the mortgage balance of $600,000 gives you interest for the first month of $2,250. Your first monthly payment of $3,040 is first applied to the interest and the remaining $790 is applied to reduce the mortgage principal.

Repeated Process

The process repeats itself for every monthly period based on the new mortgage principal balance. A typical mortgage will have large interest charges at the beginning since the principal amount is at its largest. As you pay down the principal with part of your mortgage payment, the interest charges reduce gradually and more of your payment is applied to reducing the principal.

Annual Percentage Yield

Sometimes the banks will provide the mortgage interest and the annual percentage yield (APY). The APY is a result of taking the mortgage interest rate divided by 12 and applying the result to each period of one month. Taking this monthly rate and compounding it over 12 months gives you the annual percentage yield, using the formula (1 + i/12)^12 - 1, where i is the mortgage interest rate. A mortgage interest rate of 4.5 percent gives an annual percentage yield of (1.00375)^12 - 1 = 4.59 percent.

Daily Accrual

Although more rare, some mortgages accrue interest on a daily basis using the mortgage interest rate divided by 365. Your daily interest would be the same amount every day of the same month and at the end of the month your monthly payment is applied to the total interest for that month. The result is your monthly interest charges vary depending on the number of days in the month.

If you took out your mortgage on Feb. 1 in a non-leap year, your daily interest accrual on the $600,000 mortgage would be (.045 / 365) * $200,000 = $73.97 per day. Over 28 days your monthly total interest would be 28 x $73.97 = $2,071.16.

Daily accrual in theory should average out to the same amount of interest charges as monthly, except that on a 30-year mortgage you will experience 7 or 8 leap years and that extra day of interest in February is not accounted for in a formula where you divide by 365. The result is you will pay a few days’ worth of extra interest overall when using the daily accrual method.