Simple interest does not always mean unchanged principal
On an outstanding-balance simple-interest loan, interest is calculated using the principal that remains during the relevant accrual interval. When a payment reduces that principal, later interest can fall. This differs from calculating P × r × t on the original amount for the entire term while ignoring repayments. The formula can be correct for each interval and still be misapplied to the whole loan.
CFPB distinguishes simple-interest auto loans from precomputed-interest arrangements. The actual agreement controls accrual, dates and allocation. This guide uses a deliberately simplified daily example to explain the mechanism; it is not a payoff quote or a recommendation to change payment dates. It does not account for every charge, grace-period rule or loan product.
Use a separate row whenever the principal changes
For an interval with constant principal B, annual decimal rate r, elapsed days d and a specified 365-day basis, interest is B × r × d/365. At an invented 7.3 percent annual rate, a $10,000 balance accrues $2 per day under that basis. Thirty days therefore creates $60 of interest, before any fees or payments are applied.
The day basis is part of the assumption, not a universal instruction for every lender. Contracts may specify another convention or deal differently with dates and rounding. Write the opening balance, interval start and end, counted days and rate basis together. A bare monthly payment number cannot reproduce a daily-accrual ledger without the dates that give each interval its length.
Split a payment between accrued interest and principal
Assume no fees and that a $500 payment after the first thirty days covers the $60 accrued interest before reducing principal. Principal reduction is $500 − $60 = $440, leaving $9,560. The next thirty-day interval then produces $9,560 × 0.073 × 30/365 = $57.36 of interest. The payment did not reduce principal by the full $500.
The second payment of $500 would reduce principal by $442.64 under the same assumptions, leaving $9,117.36. This two-row example shows why a payment's interest share can decline as principal is repaid. It does not establish the payment amount a lender requires or guarantee this allocation where unpaid charges or other contract terms intervene.
Compare a larger principal-reducing payment at the same date
Keep the same opening loan and first thirty days, but suppose the first payment is $1,000 rather than $500. Interest remains $60 for that already completed interval. Principal falls by $940 to $9,060. The next thirty-day interest is $54.36, which is $3 less than the $57.36 generated by the smaller first payment.
The extra $500 saves $3 over that next specified interval, not $500 of immediate interest. Its longer-run effect depends on every later payment and interval. Compare matched dates and assumptions when evaluating alternatives. If a servicer holds an excess payment for a future installment rather than applying it to principal as assumed, the balance path can be different.
Explain timing changes with the actual calendar interval
If $10,000 remains outstanding for forty days at the same hypothetical rate, interval interest is $80 rather than $60. With a $500 payment and no fees, only $420 reduces principal, leaving $9,580. That is a different accrual interval, not proof that the annual rate increased. Payment timing changes the number of days for which a balance remains outstanding.
To compare early and later payments fairly, carry both ledgers to the same final date and include all intervals. Do not compare a twenty-day period with a thirty-day period as though they cover equal time. A late payment may also create charges or consequences outside this interest illustration; this article does not determine contractual grace periods or authorize delaying a required payment.
Keep accrued interest and unpaid principal conceptually separate
Simple daily interest does not mean that unpaid interest can always be ignored. Maintain an accrued-interest record and apply payments according to the contract. If a payment is insufficient to cover the amount due, the handling of the shortfall needs the actual terms. Do not automatically capitalize it as principal unless the modeled agreement specifies that treatment.
Similarly, do not force a fixed-payment amortization formula onto an irregular daily schedule merely because both loans are called simple interest. The ordinary Loan Calculator assumes equal monthly periods and a rate divided by twelve. That can be a useful separate illustration, but its schedule is not automatically a reproduction of a daily-interest agreement with varying dates.
Use the Simple Interest Calculator to verify individual intervals
For the first interval, enter $10,000, 7.3 percent and thirty supplied days on a 365-day basis to verify $60. For the next interval after the $500 payment, enter $9,560 with the same rate and day count to verify $57.36. The principal must be updated between runs; the tool does not infer the payment or maintain the loan's evolving account.
Its balance result means entered principal plus interest for that isolated fixed-principal interval. It is not the remaining principal after a payment, nor a lender's settlement amount. The interface has no field for a sequence of payment dates, allocation rules or fee balances. A separate row-by-row ledger is needed when those details are central to the question.
Reconcile the worksheet with the servicer's record
A useful check lists each opening principal, accrual interval, interest, fees, payment allocation and closing principal. Compare discrepancies first by dates, day-count basis and rounding, then by allocation and charges. Preserve the original observations instead of changing the rate to force a matching total. A difference can reveal a missing contract assumption rather than a calculator defect.
This explanation is educational and is not financial or legal advice. It does not determine a required payment, authorize a prepayment or estimate penalties. For an actual loan, use the provider's agreement, statements and payoff information, and obtain qualified assistance where appropriate. The central lesson is that principal changes require new intervals; an unchanged-principal total cannot represent repayments it never modeled.