How to use the rule of 78 interest rebate calculator
- Enter the amount financed, the yearly rate and the number of monthly payments. These give the payment and the total finance charge.
- Enter the payment number you will pay off after. For example, 12 means you make 12 payments and settle the rest with the next one.
- Read the interest rebate, the payoff under the Rule of 78 and the payoff under simple interest, and compare them.
- Scroll to the month by month table to see how many dollars of interest each method assigns to each month.
Formula
Sum of digits S = n x (n + 1) / 2
Interest in month k = finance charge x (n - k + 1) / S
Rebate after m payments = finance charge x (n - m) x (n - m + 1) / (n x (n + 1))
Payoff = remaining payments - rebate
The finance charge is the payment times n minus the amount financed. The payment is rounded to the cent first, as it would be on a contract.
A $12,000 loan at 9% for 36 months, paid off after 12 payments
The payment is $381.60 and the finance charge is 36 x $381.60 - $12,000 = $1,737.60. The sum of digits for 36 months is 666. Month 1 is assigned 36/666 of the charge, which is $93.92, month 2 gets 35/666, which is $91.32, and month 36 gets only $2.61.
After 12 payments, 24 remain. The rebate is $1,737.60 x 24 x 25 / (36 x 37) = $782.70. The remaining payments total 24 x $381.60 = $9,158.40, so the payoff is $9,158.40 - $782.70 = $8,375.70. A simple interest loan with the same payment would be paid off with $8,352.79, so the Rule of 78 costs $22.91 more.
How the Rule of 78 assigns interest
The rule is a way to spread a fixed finance charge across the months of a loan. It front-loads the charge: the first month takes the largest share and the last takes the smallest, in proportion to the digits 1 through n added together. The name comes from the 12 month case, where the digits add to 78.
A simple interest loan earns interest on the balance still owed, which also falls over time, but less steeply than the digit weights. In the middle of the loan the two methods differ most, and at the very start and end they agree. For this reason, early payoff on a Rule of 78 loan returns a little less interest to you.
Where this matters
The method shows up in older installment contracts and in some short consumer loans. In some places it is limited for long loans or banned for certain kinds of credit, and a contract states the payoff method it uses. Read yours before you rely on any result on this page.
For the cost of a quote that uses a flat rate, see the Add-On Interest Loan Calculator. For a standard schedule, use the Amortization Schedule Calculator or the Loan Calculator.
Assumptions and limits
- The loan has equal monthly payments and a fixed rate, and the payment is rounded to the cent.
- The finance charge is the total of payments minus the amount financed, with no separate fees or insurance.
- The simple interest comparison uses the same rounded payment and monthly interest on the unpaid balance.
- The payoff does not include any prepayment fee, per diem interest or other charges your lender may add.
Frequently asked questions
Why is it called the Rule of 78?
For a 12 month loan, the digits 1 to 12 add up to 78. The first month is assigned 12/78 of the finance charge, the second 11/78, and so on down to 1/78. The same idea works for any term using that term's sum of digits.
Does the Rule of 78 change what I pay if I never pay early?
No. If you keep the loan to the end, you make every payment and the total finance charge is the same under any method. The rule only matters for how much interest is returned when the loan is paid off early.
Is the rebate the same as the interest I save?
It is the part of the finance charge that is treated as not yet earned at the payoff date. Under the Rule of 78 that figure is smaller than the interest a simple interest loan would not yet have accrued, which is why the payoff is higher.
Can I use the numbers on a real payoff?
Use them to check a figure. Your lender may add fees or round differently, and the contract decides the payoff amount. Ask for a written payoff quote before you pay.