finance calculator
Loan Payment Calculator
Estimate fixed-rate loan payments, affordable principal, payoff term, remaining balance, total paid, and interest.
Fixed-rate estimate
Calculate loan payments
Estimated result
Enter loan assumptions and choose Calculate.
Formula version 1.0.0 · Fixed rate · End-of-period payments.
Amortization model
Loan payment formula and assumptions
For principal P, periodic rate r, and n end-of-period payments: payment = Pr/(1−(1+r)^−n). At zero interest, payment is P/n.
Rate and term conversion
Periodic rate = annual nominal rate ÷ payments per year. Periods = years × payments per year.
Remaining balance
Bₖ=P(1+r)^k−payment((1+r)^k−1)/r.
What is excluded
Unless entered as financed fees, the estimate excludes taxes, insurance, penalties, variable rates, lender-specific rounding, and regulatory disclosures.
Important
This is an educational estimate, not a loan offer or financial advice. Compare results with the lender's official schedule.
How to use this calculator
- Choose the loan result you want in Calculation type.
- Enter every displayed amount, annual percentage rate, term, and payment frequency.
- Use Fees added to principal only for fees financed into the loan balance.
- Select Calculate, then review the estimate, total interest, periods, steps, and assumptions.
Symbols and units
| Symbol | Meaning | Unit or domain |
|---|---|---|
P | Principal plus any financed fees | One consistent currency |
r | Periodic nominal interest rate | Annual percent ÷ 100 ÷ payments per year |
n | Number of end-of-period payments | Count |
PMT | Payment each period | Same currency as P |
Bₖ | Balance after k payments | Same currency as P |
Checked examples
Monthly payment
Inputs: Principal 200,000; rate 6%; 30 years; 12 payments/year; fees 0
Calculation: r=.06/12; n=360; PMT=Pr/(1−(1+r)^−n)
Result: Approximately 1,199.10 per month
The result excludes taxes, insurance and lender-specific charges.
Check: loan-payment.test.ts — calculates a standard amortized payment
Zero-rate loan
Inputs: Principal 12,000; rate 0%; 2 years; 12 payments/year
Calculation: 12,000 ÷ 24
Result: 500 per month
At zero interest, principal is divided evenly across periods.
Check: loan-payment.test.ts — handles zero-interest payment
Assumptions, rounding, and limits
- Fixed nominal annual rate and equal end-of-period payments.
- Payment frequency and compounding frequency are treated as the same.
- Amounts use one currency; no currency conversion occurs.
- Taxes, insurance, penalties, variable rates and unentered fees are excluded.
- Displayed currency results round half-up to two decimals; the formula retains working precision.
- Educational estimate only; lender disclosures and schedules control.
Frequently asked questions
Does this include taxes and insurance?
No. Only principal and explicitly entered financed fees are modeled.
Why can a lender quote differ?
Payment timing, day-count rules, fees, insurance, taxes and lender rounding can differ from this fixed-rate model.
Can I use a zero interest rate?
Yes. The calculator uses principal divided by the number of payments.
Sources and review
- OpenStax: Loan Amortization — Section 8.3; accessed 2026-10-25
- Consumer Financial Protection Bureau: How mortgage lenders calculate monthly payments — Payment calculation overview; accessed 2026-10-25
- Formula version
- loan.payment@1.0.0
- Formula review
- Equatara formula review
- Editorial review
- Equatara editorial review
- Last verified
- 2026-10-25
- Applicability
- Global fixed-rate ordinary-annuity estimate; not a jurisdictional disclosure.
- Next review
- Domain review by 2027-04-25 or on material change.
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Found a problem?
Report a formula, result, example, source, or accessibility issue through the calculator correction process. Do not include sensitive input values.