Loan Payment Calculator
Understand how a fixed monthly loan payment is calculated, which assumptions matter, and why a formula estimate can differ from a lender schedule.
This guide explains the standard payment formula for a fully amortizing loan with a fixed nominal annual rate, equal monthly payments, and payments made at the end of each month. It shows principal-and-interest results only. Results are educational estimates, not a lender quote.
Informational nature of the result
Important: figures on this page are educational estimates for planning and comparison. They are not a credit offer, binding quote, affordability decision, tax opinion, investment recommendation, or legal advice. Always compare any estimate with the lender’s repayment schedule and contract before committing.
What this calculation includes and excludes
Includes (under the stated assumptions):
- Principal (loan amount)
- Interest at a fixed nominal annual rate converted to a monthly rate
- Equal monthly payments over a fixed number of months (standard amortizing annuity)
Does not include:
- Origination fees, arrangement fees, or other lender charges
- APR disclosure adjustments that embed fees or product rules
- Taxes, insurance, escrow, or compulsory add-ons
- Variable-rate resets, interest-only periods, balloons, or payment holidays
- Early-repayment penalties or contract-specific recalculation rules
- Currency conversion or inflation adjustments
Assumptions used in this guide
- Fully amortizing loan: payments cover interest due for the period and reduce principal to zero by the final payment (no balloon remaining).
- Fixed nominal annual interest rate for the whole term.
- Monthly compounding approximation: monthly rate = nominal annual rate ÷ 12 ÷ 100.
- Payments at the end of each month (ordinary annuity).
- Same currency for principal and payment; no FX.
- No fee or insurance cash flows in the payment amount.
What is the loan installment?
The loan installment (monthly payment) is the amount paid regularly to the lender during the repayment period. Under this method, each installment has two parts:
- Interest — cost of borrowing for the period on the outstanding balance
- Principal — the portion that reduces the amount still owed
Early in the schedule, interest usually takes a larger share; later payments shift more toward principal. Understanding that split helps cash-flow planning even when the total payment stays constant.
Formula and variable definitions
For a positive monthly interest rate, the equal monthly payment is:
Monthly payment = P × [r(1 + r)n] ÷ [(1 + r)n − 1]
- P — principal (amount borrowed)
- r — monthly interest rate in decimal form (nominal annual rate ÷ 12 ÷ 100)
- n — total number of monthly payments
If the periodic rate is zero, use Monthly payment = P ÷ n. The standard annuity equation requires that separate zero-rate case.
Complete example: €10,000 · 6% · 36 months
Hypothetical inputs: principal €10,000, nominal annual interest 6%, term 3 years (36 months). Fees, taxes, and insurance are excluded.
- Monthly rate r = 6% ÷ 12 = 0.5% = 0.005
- Number of payments n = 36
- Unrounded monthly payment = €304.2193745156
- Displayed monthly payment (2 decimals) = €304.22
- Total of 36 payments using the unrounded result = €10,951.90
- Estimated total interest = €10,951.90 − €10,000.00 = €951.90
If every displayed payment were simply multiplied after rounding, €304.22 × 36 = €10,951.92. A real lender may adjust the final payment or use different rounding and day-count rules, which is one reason its schedule can differ by a small amount.
Even a small difference in rate or term can change total interest materially. Re-run the estimate whenever the rate, fees, or term change—and still treat the output as an estimate until the lender schedule is confirmed.
Limitations
- APR and fees: APR may include charges or disclosure assumptions that this principal-and-interest formula does not model.
- Variable rates: future rate changes require a period-by-period schedule, not one fixed rate.
- Balloon or interest-only structures: these require different cash-flow and remaining-balance logic.
- Early repayment: prepayments, penalties, and recalculation rules depend on the contract.
- Lender rounding and dates: day-count conventions, payment dates, and final-payment adjustments may change totals.
- Taxes and insurance: excluded; they vary by asset, borrower, and jurisdiction.
- Jurisdiction: lending disclosures, fees, and consumer protections are not universal.
Continue the calculation review
Browse related interest and capital tools in the calculator collection, then compare any estimate with the lender’s own schedule before you commit.
FAQ
What is a loan installment?
It is the regular amount paid to the lender during the repayment period. Under this guide’s method, each installment covers period interest and a principal reduction, with a constant total payment when the rate and term are fixed.
What interest rate should I enter?
Use the nominal annual interest rate only when the calculation assumes monthly compounding and monthly payments. APR may include fees or use disclosure rules that are not represented by this formula, so do not substitute APR without checking the lender’s definition.
Does the payment include fees, taxes, or insurance?
No. The formula covers principal and interest under the stated assumptions. Add lender fees, taxes, insurance, and other charges separately using documents that apply to the loan and jurisdiction.
What happens when the interest rate is zero?
When the periodic rate is zero, divide the principal by the number of payments. The standard annuity equation cannot divide by a zero rate, so this separate case is required.
Can this method model variable rates or balloon payments?
Not as one fixed calculation. Variable-rate loans need a schedule of rate changes; balloon structures need the remaining balance modeled explicitly.
Is the result a lender quote?
No. It is an educational estimate. Lender schedules may differ because of fees, day-count rules, payment dates, rounding, insurance, taxes, or contract terms.