# Actuarial Method of Interest Calculation

​​​​There are three basic methods of determining the amount of interest that will be charged on a loan.  These three methods are commonly known as the rule of 78's, simple interest method, and actuarial method.

​The actuarial method is used by some lenders to calculate the refund of the interest charge when a pre-computed consumer loan is prepaid in full.  When a consumer loan is pre-computed, the customer promises to pay the total of payments, which is the sum of the amount financed (principal) and the interest charge for the full term of the transaction. The creditor then is required to allow a refund of a portion of the pre-computed interest charge if the loan is prepaid in full.

The following is an example of a consumer loan:

 ​Amount Borrowed​​​ ​\$5,000 ​Annual Interest Rate ​10% (or 10% ÷ 12 months = .8333% per month) ​Term of Loan ​12 months ​Monthly Payment ​\$439.58 ​Finance Charge ​\$274.96 ​Total of Payments ​\$5,274.96

The following schedule shows how interest would be calculated on our example loan.  For sake of simplicity, we will assume 360 days per year with 30 days between the contract date and the first due date and 30 days between each monthly due date.  To determine the interest charge for a month, multiply the outstanding balance for the month by the monthly interest rate.  For example, the first month’s interest charge would be:  \$5000 x .8333% = \$41.67.  Subtract the interest charge from the payment amount to determine the amount of your principal reduction, \$439.58 - \$41.67 = \$397.91.  Subtract the principal reduction from the current balance to determine next month’s outstanding balance.

 ​Month ​Payment ​InterestCharged ​AccumulatedInterest Charge ​PrincipalReduction ​OutstandingBalance ​0 ​ ​ ​ ​ ​\$5,000.00 ​1 ​439.58 ​41.67 ​41.67 ​397.91 \$​4,602.09 ​2 ​439.58 ​38.35 ​80.02 ​401.23 ​\$4,200.86 ​3 ​439.58 ​35.01 ​115.03 ​404.57 ​\$3,796.29 ​4 ​439.58 ​31.64 ​146.67 ​407.94 ​\$3,388.35 ​5 ​439.58 ​28.24 ​174.91 ​411.34 ​\$2,977.01 ​6 ​439.58 ​24.81 ​199.72 ​414.77 ​\$2,562.24 ​7 ​439.58 ​21.35 ​221.07 ​418.23 ​\$2,144.01 ​8 ​439.58 ​17.86 ​238.93 ​421.72 ​\$1,722.29 ​9 ​439.58 ​14.35 ​253.28 ​425.23 ​\$1,297.06 ​10 ​439.58 ​10.81 ​264.09 ​428.77 ​\$868.29 ​11 ​439.58 ​7.24 ​271.33 ​432.34 \$​435.95 ​12 ​439.58 ​3.63 ​274.96 ​435.95 \$​0 ​Totals ​5,274.96 ​274.96 ​ ​5,000.00​ ​

When the actuarial method is used, follow the steps below to determine the amount of interest that can be assessed on the loan:

1. Determine which scheduled due date is nearest to the payoff date of the loan.  For example, assume you pay off the sample loan on a date nearest the fifth scheduled due date.
2. Next, read across the line on the schedule which pertains to the fifth scheduled due date.  You will notice that the accumulated finance charge which relates to the fifth month is \$174.91.  This is the amount of interest you will be charged.  By subtracting the \$174.91 figure from the total finance charge you will determine the amount of the finance charge refund (\$274.96 - \$174.91 = \$100.05).

When paying off the loan near the fifth due date, the interest charge will be \$174.91 regardless of how the previous payments were made.  This is because the actuarial method assumes all payments are made as scheduled.  Payments are made “as scheduled" when they are made according to the terms of the contract.  Making payments earlier than scheduled, or in amounts greater than scheduled, will not affect the interest charge for the period prior to the payoff date.

The only factor that affects the amount of interest to be charged is the amount of time the loan is outstanding.  Assume two people each obtain a loan, similar to our example, and both borrowers pay the loan off on the third due date.  Let's also assume one borrower made the first two payments as scheduled and the other borrower made the first two payments 10 days prior to the due date and in an amount twice that of the scheduled payment amount.  Both borrowers will be assessed the same amount of interest (\$115.03) because both loans were outstanding for the same amount of time.

​When payments are made as scheduled, the amount of the interest charge will be approximately the same under all three of the basic interest methods.  Only when payments are not made as scheduled can significant differences occur between the three methods.

The Wisconsin Consumer Act was amended, effective August 1, 1987, to require the creditor to use either an actuarial method or a simple interest method to calculate the interest refund on transactions where the initial term is 37 months or more, or the amount financed is \$5000 or more.  For pre-computed consumer credit transactions not meeting those conditions, the rule of 78's method can be used to calculate the interest refund.

Use of the actuarial method is referred to in Wis. Stat. s. ​422.209(2)(b)1