Late & Partial Loan Payment Interest Formula

Daily interest when a payment changes principal

For a simple-interest loan, a mid-period principal payment creates two interest periods: before the payment, when the old balance applies, and after it, when the updated balance applies. The payment must actually be credited to principal on its effective date.

B₁ is the balance before the payment; B₂ is the balance after the principal credit; r is the annual rate as a decimal; d₁ and d₂ are accrued calendar days; Y is the contract's day-count basis (often 360 or 365).

Worked example: a $5,000 principal-only payment

Assume $30,000 principal at 8% Actual/365 on January 1. A separately identified $5,000 principal-only payment becomes effective January 16. Calculate interest through February 1, excluding January 1 and including February 1.

The daily rate changes because principal decreases on January 16. There is no double-counting of January 16: the first period ends when the payment posts, and the second begins immediately afterward. Totals may vary by a cent if the lender rounds interest daily instead of only at the end of the period.

What if it is an ordinary partial payment instead?

Do not automatically reduce principal by the full payment. Under an illustrative interest-first allocation, interest accrued to the payment date is paid first, and only the remainder goes toward principal. Some agreements, servicers, or consumer protections may require a different allocation, or permit holding an incomplete payment pending a full periodic installment. Read the note and posting history before calculating.

How late payments affect payoff

When a payment arrives later than expected, more days of interest may accrue on the prior principal balance. Late fees, default rates, compounding, grace periods, and payment posting rules are separate contractual issues; they are not automatically included in the daily-simple-interest formula.

Run actual payment dates

Our Private Loan Payoff Statement Generator calculates simple-interest accrual across dated payments using an explicit illustrative payment-allocation rule. The Irregular Payment Loan Calculator explores changing payment dates and amounts. For long-term saved records, see Private Loan Manager.

FAQ: should the payoff interest rate use 360 or 365?

Use the basis specified by the loan agreement or confirmed by the servicer. Actual/360 generally produces more interest per day for the same stated annual rate than Actual/365. The result also depends on which accrual dates are included.