— Loans & Debt
Interest Rate Calculator (from your payment)
Given a loan amount, a payment and a tenure, what rate are you really paying? Back it out, check it against the quote, and add fees for the true APR.
Implied annual rate
8.01%
- Total interest
- $5,420
- Total payment
- $30,420
- Equivalent flat rate
- 4.34%
— Where the money goes
Download— How it works
There is no closed form for the rate — it is solved numerically (bisection) from the payment equation: payment = P·r·(1+r)ⁿ ÷ ((1+r)ⁿ − 1).
Reverse-engineering the rate
Sometimes you know everything about a loan except the rate — you have the amount, the payment on the statement, and the term, but the “rate” quoted feels slippery or was never clearly stated. This calculator backs out the rate you are actually paying from those three numbers. Unlike the tenure, the rate has no neat formula to rearrange: it sits inside the payment equation in a way that cannot be isolated algebraically. So the calculator solves it numerically, narrowing in on the rate that makes the payment equation balance — the same technique used to compute an APR or an investment’s XIRR.
It is a useful audit. If a lender’s “effective” rate is higher than what you were led to expect, this is how you catch it — by working backwards from what you actually pay.
Worked example — a $25,000 loan repaid with a $507 monthly payment over 5 years: The total paid is about $30,420, so roughly $5,420 is interest. The rate that fits those payments is almost exactly 8% reducing — and the equivalent flat rate is only about 4.3%, which is the number a lender might prefer to advertise.
Fees, quotes and flat rates
The implied rate is the reducing rate on the loan itself. But if there was a processing fee, your true cost is higher — enter the fee and the calculator computes the effective APR, which folds it in. Enter the rate you were quoted and it shows the gap, flagging when the rate you are really paying exceeds the advertised one. And it always shows the equivalent flat rate: the deceptively low number that produces the same interest, which is exactly why “flat” quotes sound cheaper than they are.
If you are trying to decode a flat quote rather than a reducing one, our flat-vs-reducing calculator is built for that — it converts in both directions and shows the cost gap.
— Reader questions
How do I find the interest rate from my payment?
Enter the loan amount, the payment and the tenure, and the calculator solves for the annual reducing rate that fits — the rate that makes the payment equation balance. There is no formula to isolate the rate directly, so it is found numerically, the same way an APR is.
Why is there no formula for the interest rate?
Because in the payment equation the rate appears both as a multiplier and inside a power, so it cannot be algebraically separated out the way the tenure can. The standard approach is a numerical solver that converges on the rate — which is exactly what this calculator uses.
What is the difference between the implied rate and the APR?
The implied rate is the reducing rate on the loan amount alone. The APR also includes fees — it is the rate on the money you actually received after the fee. Enter a processing fee and the calculator shows both, with the APR sitting above the implied rate.
What is the equivalent flat rate?
It is the flat rate that produces the same total interest as your reducing rate — always a lower-looking number, because a flat rate is charged on the original principal throughout. The calculator shows it so you can see why a flat quote sounds cheaper than the reducing reality.
Can I check this against the rate I was quoted?
Yes. Enter the quoted rate under the advanced options and the calculator shows the gap between it and the rate you are actually paying, flagging when the implied rate is higher — a quick way to audit a lender’s effective charge.