Unearned Interest

Unearned Interest: What it Is, How It Works, and How to Calculate It

Definition

Unearned interest (also called unearned discount) is interest that a lender has collected but has not yet recognized as income. Initially recorded as a liability, it is recognized as income over time as the interest is earned. If a borrower repays a precomputed loan early, the lender must refund the unearned interest.

How it arises

• Many loans require payments at the beginning of each month. Part of each payment is interest that covers the borrower’s use of funds for that entire month.
• Because that interest is paid in advance, the lender cannot immediately recognize it as earned income — the loan principal has not been outstanding for the full period.
• Accounting entry when interest is prepaid: debit Cash; credit Unearned Interest (liability).
• Over time the unearned interest is amortized into interest income (debit Unearned Interest; credit Interest Income).

Example: If a borrower makes a $1,200 monthly payment where $240 is interest, that $240 is prepaid interest for the entire month and is recorded as unearned until the month passes.

If a loan is paid off early, the borrower receives a refund equal to the amount of unearned interest remaining. For example, on a 36-month loan paid off after 30 months, the borrower would be refunded six months of interest that had not yet been earned.

Amortization of unearned interest

Unearned interest is moved from liability to revenue gradually over the life of the loan. Each accounting period a portion of the unearned interest balance is recognized as interest income, matching revenue to the period in which it is earned.

Calculating unearned interest (Rule of 78)

For precomputed loans (loans with finance charges calculated up front), unearned interest can be estimated using the Rule of 78. This method allocates more of the finance charge to earlier payments, so the rebate for early payoff is smaller than with straight-line allocation.

Formula:
Unearned interest = F × [k(k + 1) / n(n + 1)]

Where:
– F = total finance charge = n × M − P
– M = regular monthly loan payment
– P = original loan amount
– k = remaining number of payments after the current payment
– n = original number of payments

Worked example:
– Original loan: $10,000
– Term: 48 months
– Monthly payment: $310
– Borrower repays after 36 months (so k = 12 remaining payments)

Step 1: Total finance charge
F = (48 × $310) − $10,000 = $14,880 − $10,000 = $4,880

Step 2: Apply Rule of 78 factor
k(k + 1) = 12 × 13 = 156
n(n + 1) = 48 × 49 = 2,352
Factor = 156 / 2,352 ≈ 0.0663

Step 3: Unearned interest
Unearned interest = $4,880 × 0.0663 ≈ $323.67

Key takeaways

• Unearned interest is prepaid interest recorded as a liability until it is earned over time.
• If a precomputed loan is paid off early, the borrower is due a refund of the unearned interest.
• The Rule of 78 provides a common method to calculate the rebate on precomputed loans; it allocates more finance charge to earlier payments.