Interest is Paid in Arrears
In the United States, interest is paid in arrears. This means your principal and interest payment will pay the interest for the 30-day period immediately preceding your payment due date.
For example, say your payment of $599.55 is due December 1. Your loan balance is $100,000, bearing interest at 6% per annum, and amortized for 30 years. When you make your payment for December 1, you are paying the interest for the entire month of November, all 30 days.
If you are closing your loan on October 15th, you will prepay interest from October 15th through October 31st to the lender. It may seem like you get 45 days free before your first payment is due on December 1, but you are not. You will pay 15 days of interest before you close and another 30 days of interest when you make your first payment.
Computing Your Principal Unpaid Balance
If you want to know your unpaid principal loan balance that is remaining after you make your first payment, it is easy to compute. First, take your principal loan balance of $100,000 and multiply it times your 6% annual interest rate. The annual interest amount is $6,000. Divide the annual interest figure by 12 months to arrive at the monthly interest due. That number is $500.00.
Since your December 1 amortized payment is $599.55, to figure the principal portion of that payment, you would subtract the monthly interest number ($500) from the principal and interest payment ($599.55). The result is $99.55, which is the principal portion of your payment.
Now, subtract the $99.55 principal portion paid from the unpaid principal balance of $100,000. That number is $99,900.45, which is the remaining unpaid principal balance as of December 1. If you are paying off a loan, you must add daily interest to the unpaid balance until the day the lender receives the payoff amount.
Note: With each consecutive payment, your unpaid principal balance will drop by a slightly higher principal reduction amount over the previous month. This is because although the unpaid balance is computed using the same method every month, your principal portion of the monthly payment will increase while the interest portion will get smaller.
You know now that your unpaid principal balance after your December payment will be $99,900.45. To figure your remaining balance after your January 1 payment, you will compute it using the new unpaid balance:
$99,900.45 x 6% interest = $5,994.03 ÷ by 12 months = $499.50 interest due for December. Your January payment is the same as your December 1 payment because it is amortized. It is $599.55. You will subtract the interest due for December of $499.50 from your payment. That leaves $100.05 to be paid to principal on your loan.
Your balance as of December 1 is $99,900.45, from which you subtract the principal portion of your January 1 payment of 100.05. This equals $99,800.40 as your new unpaid principal balance.
Computing Daily Interest
To compute daily interest for a loan payoff, take the principal balance times the interest rate and divide by 12 months, which will give you the monthly interest. Then divide the monthly interest by 30 days, which will equal the daily interest.
Say, for example, that your uncle gives you $100,000 for a New Year's Eve present and you decide to pay off your mortgage on January 5th. You know you will owe $99,800.40 as of January 1. But you will also owe 5 days of interest. How much is that?
$99,800.40 x 6% = $5,988.02. Divide by 12 months = $499. Divide by 30 days = $16.63 x 5 days = $83.17 interest due for five days.
You would send the lender $99,800.40 plus $83.17 interest for a total payment of $99,883.57.
At the time of writing, Elizabeth Weintraub, DRE # 00697006, is a Broker-Associate at Lyon Real Estate in Sacramento, California.