What Is Unearned Interest?

Definition and Example of Unearned Interest

After a lender collects interest on a loan, it is either earned or unearned. Unearned interest is exactly as it sounds—interest that is yet to be earned or converted into income. Enough time must pass before the interest can be recorded as income (or earned); until then, it is called unearned interest. 

• Alternate name: unearned discount

For example, if you have a loan payment of $200 due on the first of the month and $125 of your payment is applied to interest, then the $125 is considered unearned interest; the lender cannot count it as income or earned interest until the last day of the month.

How Unearned Interest Works

When a lender collects payment at the beginning of the month, it includes both a portion of the principal balance and a prepayment of interest. The interest compensates the lender for lending the money to the borrower. However, because the interest is paid in advance for the month ahead, it can’t initially be counted as income or earned interest. Instead, the lender records it as unearned until the month has ended or once the loan principal is outstanding long enough to earn interest. 

Lenders typically structure loan payments to include a higher portion of interest early on. Often, the majority of a payment will be applied to interest rather than the principal balance. If the principal balance hasn’t been outstanding long enough, the greater portion of interest is considered unearned. As the balance decreases, the earned interest charges become less each month.

In mortgage loans, a more significant portion of the monthly payment will be devoted to interest during the first few months of the loan period. This accounting technique helps lenders amortize the loan.

For accounting purposes, lenders mark unearned interest on their ledger as a debit to the cash account and a credit to the unearned interest income account. This recognizes the interest as income that has yet to be recorded. 

The Rule of 78

To calculate unearned interest, lenders typically use the Rule of 78. Lenders apply the Rule of 78 when a borrower pays off the balance of a pre-computed loan or account early. A pre-computed loan has predetermined interest rates or equal monthly installments. 

The Rule of 78 is the sum of the digits in the months of the year. For example: 1 + 2+ 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 = 78. 

If you have a 12-month contract and pay the loan off after three months (12 + 11 + 10 = 33), then the lender has earned and is entitled to keep 33/78 or 42.31% (33 divided by 78) of the finance charges. That means that 45/78 (78 - 33)  is unearned, and 57.69% is eligible for a rebate. 

The same pattern applies to loan terms longer than 12 months. For example, a 24-month loan would have a sum of digits and a denominator that equals 300. Therefore, the value of the first month would be 24/300.

Instead of long math, the formula N/2 x (N + 1) is used to calculate the denominator quickly, where n equals the number of payments. So, for a 36-month loan: 36/2 x (36+1), 18 x 37 = 666.

Now let’s apply it to a real-life scenario. Let’s say a borrower took out a $15,000 car loan to be repaid in 36 monthly installments of $500 (including interest), but they paid the loan off early at 30 months. Using the Rule of 78s, we know that a 36-month loan has a 666 sum of digits for the denominator.

Therefore, paying off the loan in the 30th month would equal 645/666 in earned interest, leaving 21/666 or 0.03153 in unearned interest. Now, multiply that by the finance charge, and you have the amount of unearned interest due back to the borrower. 

The finance charge formula looks like this: n x m – p  = f

(number of payments x regular monthly payment) – total loan amount = finance charge

(36 x $500) – $15,000 = $3,000

The finance charge is $3,000, and the unearned interest due is 0.03153.

$3,000 x  0.03153 = $94.59

Another way to calculate the Rule of 78 or unearned interest, is by using this formula:

[k(k + 1) / n(n + 1)] x F = u

K = remaining payments 

N = number of payments

F = finance charge

U = unearned interest

This portion will equal the Rule of 78 decimal [k(k + 1) / n(n + 1)] 

Now let’s use it to calculate the unearned interest using the same car loan example from above:

[k(k + 1) / n(n + 1)] x F = u

[6(6+1) / 36(36+1)] x $3,000 = u, or [(6x7) / (36x37)] x $3,000 = u

(42 / 1332) x $3,000

0.03153 x $3,000 = $94.59

The unearned interest formula may be expressed in a few different ways, but the result is the same. 

Per the Housing and Community Development Act of 1992, a creditor cannot use the Rule of 78 to refund unearned interest on loan terms over 61 months. Instead, they must use another actuarial method favorable to the consumer.