How can I find the rate if the lender only quotes a monthly payment?

Solve for it. The annuity formula cannot be rearranged for the rate in closed form, so this page brackets the answer numerically. Comparing a quoted payment against the rate it implies is the fastest way to find a fee hidden in the instalment.

Why does my computed rate differ from the one advertised?

Usually because fees are being repaid inside the instalment, or the advertised figure is a flat rate rather than a reducing-balance one. A flat 8% is roughly a reducing-balance 14.5% over five years.

Finance & Loansloans

Loan Interest Rate Calculator

Recover the interest rate a lender is actually charging from the loan amount, the EMI and the term. Useful when a quote gives you a payment but is vague about the rate.

Also called: find interest rate from emi, implied interest rate, what rate am i paying.

Implied interest rate

8.01%

Paying $507 a month for 5 years on a loan of $25,000 implies an annual rate of 8.01%.

Total interest

$5,420.00

Total repayment

$30,420.00

How this is calculated

An estimate, not an offer or a guarantee. Projected returns assume the rate you entered holds for the whole term, which no market does.

Method and background

This is what the calculation gives for the numbers you entered. It is an estimate, not advice, and it knows nothing about your situation beyond those numbers. Rules for United States change on a published schedule; the effective date is shown on every rule-based tool.

How this is calculated

There is no closed form for i, so the engine brackets the answer and bisects. Bisection is slower than Newton–Raphson and cannot fail to converge on a bracketed sign change, which is the right trade here: a rate that is always right beats one that is usually faster.

solve for i: P * i(1+i)^n / ((1+i)^n - 1) = E

E: The equal periodic instalment (currency)
P: Principal: the amount borrowed (currency)
i: Monthly interest rate = annual rate ÷ 12 ÷ 100 (decimal)
n: Total number of monthly instalments (months)

Full derivation: Why an 8% flat loan is really a 14.13% loan

Worked examples

Each of these is asserted on every build. If a change to the engine ever moved one of these answers, the build would fail before the page could print it.

US case at 7.5%

Loan amount: $35,000.00
EMI: $701.32
Tenure: 5 years

Implied interest rate7.5%

inverse of Excel PMT(7.5%/12, 60, -35000)

Open this example

Method and limits

What it assumes

Interest compounds monthly on the reducing balance.
The rate stays fixed for the whole term. Floating-rate loans reset periodically.
Processing fees, insurance and statutory charges are excluded.

What it deliberately does not model

Recovers the rate implied by the payment schedule alone. Fees paid up front raise the true cost above this figure, the APR calculator includes them.

Formula version 1.0.0 · definition 1.0.0 · United States · Report a problem with this calculator

Frequently asked questions

How can I find the rate if the lender only quotes a monthly payment?: Solve for it. The annuity formula cannot be rearranged for the rate in closed form, so this page brackets the answer numerically. Comparing a quoted payment against the rate it implies is the fastest way to find a fee hidden in the instalment.
Why does my computed rate differ from the one advertised?: Usually because fees are being repaid inside the instalment, or the advertised figure is a flat rate rather than a reducing-balance one. A flat 8% is roughly a reducing-balance 14.5% over five years.