Formula and calculation method
The estimate treats the loan as an ordinary annuity with equal payments at the end of each month. For principal P, monthly rate i, and number of monthly payments n, the payment M is M = P × i ÷ (1 − (1 + i)−n). The monthly rate is the entered annual interest rate divided by 12 and 100.
At a zero rate, the payment is P ÷ n. For each month, interest equals the opening balance times i; the rest of the payment reduces principal. The final balance is set to zero after the last scheduled payment.
Assumptions and fixed values
- Loan structure: fully amortizing, fixed-rate, equal monthly payments made at each month’s end.
- User-supplied values: amount financed, nominal annual interest rate, and term. The calculator does not fetch or recommend current market rates.
- Fixed versus changing values: the formula is fixed; every material numeric value is entered by the user. No jurisdictional table or regularly changing external value is used.
- Rounding: calculations retain JavaScript double precision. Currency is rounded to cents for display, so a lender that rounds every payment period may differ by a few cents.
- Boundaries: the tool accepts positive loan amounts, rates from 0% through 100%, and whole-month terms from one month through 50 years.
Limitations and disclaimer
This estimate includes principal and interest only. It omits origination and lender fees, APR calculation, taxes, insurance, escrow, optional products, prepayments, late fees, daily-interest accrual, variable rates, balloons, and contract-specific payment allocation.
It is educational information, not financial, legal, tax, or lending advice; it is not an offer, approval, disclosure, or recommendation. Compare the estimate with the written terms supplied by a lender before making a decision.
Worked example
A $25,000 loan at a 7% nominal annual rate for five years uses a monthly rate of 0.07 ÷ 12 and 60 payments. The unrounded formula produces an estimated payment of $495.0299, displayed as $495.03, and estimated total interest of $4,701.80.
Common questions
Is the entered rate the same as APR?
Not necessarily. CFPB explains that APR can include fees in addition to interest. This calculator uses the entered rate as a nominal interest rate and does not derive APR.
Why does early interest look larger?
Interest is calculated from the remaining balance. The balance is highest near the start, so more of an equal payment goes to interest early and more goes to principal later.
Can I use this for an adjustable or balloon loan?
No. Those contracts require additional rate-reset or final payment assumptions that this fixed-rate, fully amortizing model intentionally excludes.
Related Aletheia tools
Use the Compound Interest Calculator to model savings growth, or the Date Duration Calculator for date-only elapsed-time questions.
Version and verification
Calculation version 1.0.0; formula and deterministic fixtures last verified 2026-08-05. Authority pages were retrieved 2026-08-05. Automated tests cover zero-rate, boundary, reconciliation, metadata, privacy, keyboard, responsive, contrast, and Axe behavior. Manual VoiceOver remains waived and is not claimed as passed.