Interest rate calculator from payment and term
Enter principal, equal payment, term and payment frequency. HitEquals numerically solves the periodic rate, annual nominal rate, effective annual rate, total paid and interest.
Inputs used by this calculator
Interest Rate Calculator uses the fields below. The starting values reproduce the page example; replace them with values from the same units and time period before using the result.
| Input | Starting example | Accepted value | How it is used |
|---|---|---|---|
| Loan principal | 25,000 | 0.01 to 1000000000000 | Supplies the loan principal quantity used by the published equation or result breakdown. |
| Payment each period | 500 | 0.01 to 1000000000000 | Supplies the payment each period quantity used by the published equation or result breakdown. |
| Term (years) | 5 | 0.01 to 100 | Supplies the term (years) quantity used by the published equation or result breakdown. |
| Payments per year | Monthly — 12 | Monthly — 12 · Biweekly — 26 · Weekly — 52 · 2 more choices | Supplies the payments per year quantity used by the published equation or result breakdown. |
How to find an unknown loan rate
Use the amount originally borrowed, the scheduled equal payment and the complete repayment term. Choose the actual number of payments per year; the engine searches for the rate that amortizes the balance to zero.
Rate equation
There is no simple elementary rearrangement for the rate, so the engine uses bounded bisection on the standard present-value equation.
principal = payment × (1 − (1 + r)⁻ⁿ) ÷ rnominal annual rate = r × payments/yearNominal and effective annual rates
The nominal result multiplies the periodic rate by payment frequency. The effective annual rate compounds it across one year and is therefore usually higher when the rate is positive.
Interest rate versus APR
CFPB explains that APR is broader than the interest rate because it can include certain fees and charges. This page solves only the rate inside the equal-payment equation.
When inputs cannot produce a rate
Payment must at least equal principal divided by payment count for a nonnegative rate. Inputs requiring more than 100% nominal annual interest are rejected rather than extrapolated.
What the Interest Rate Calculator answers
Find the annual interest rate implied by a loan amount, payment and term.
Use Interest Rate Calculator when you know Loan principal, Payment each period, Term (years) and Payments per year and need the relationship expressed by the published equation.
Frequency reference
| Schedule | Payments/year | Five-year payments |
|---|---|---|
| Monthly | 12 | 60 |
| Biweekly | 26 | 130 |
| Weekly | 52 | 260 |
| Quarterly | 4 | 20 |
| Annual | 1 | 5 |
Frequently asked questions
How can I calculate interest rate from a payment?
Solve the present-value equation using principal, payment count and payment amount; this calculator performs the numerical search.
Is the result APR?
No. It is the nominal note rate implied by the cash flows and excludes fees.
What is effective annual rate?
It is the one-year compounded return corresponding to the periodic rate.
Why is my payment too low?
A payment below principal divided by the number of periods cannot repay the loan at any nonnegative rate.
Can payment frequency change the result?
Yes. It changes the number of payments and how the periodic rate is annualized.
What question does this Interest Rate Calculator answer?
Find the annual interest rate implied by a loan amount, payment and term.
What to keep in mind
This solves a nominal note rate from equal payments. It is not APR and excludes fees, insurance, taxes, irregular payments and compounding outside the selected schedule.
Results are rounded for display in US format, with money in dollars and cents; CSV exports keep full calculation precision. This is a calculation summary, not an official certificate.