What the interest rate calculator does
Sometimes you know the loan amount, the monthly payment and the term, but not the rate — a dealer quote that only mentions the monthly figure, a payment plan with the rate buried in the small print, a loan statement from years ago, or a “0% finance” offer where the cash price is lower. This calculator solves for the annual interest rate from those three numbers and shows the total interest that rate implies. It runs in your browser.
Why it needs a numerical method
The payment formula gives the payment from the rate, but it cannot be rearranged to give the rate from the payment — the rate appears both inside a power and outside it. The calculator therefore uses Newton's method: guess a rate, compute the payment it would produce, compare with the actual payment, adjust the guess in proportion to the error, and repeat. It converges to within a rounding error in a handful of steps.
Payment(r) = P × r(1 + r)ⁿ / ((1 + r)ⁿ − 1)
Find r such that Payment(r) = your actual payment
$200,000 loan, $1,200/month, 360 payments → r ≈ 0.5039%/month → 6.05% annual
Total paid = 1,200 × 360 = $432,000 Total interest = $232,000Where this is useful
- Dealer and retailer finance — “$399 a month for 72 months” on a $24,000 car is 8.9% APR. Now you can compare it with your bank's offer.
- Buy-now-pay-later and instalment plans — a “no interest” plan where the cash price is 10% lower has a real rate; enter the cash price as the amount.
- Checking a statement — confirming the rate actually applied to an old loan.
- Private loans — working out the implied rate on a repayment schedule agreed between individuals.
- Leases and rent-to-own — estimating the effective rate when only the payment is quoted (with a residual value, the true rate is a little different).
Interest rate vs APR
The rate this tool finds is the rate implied by the payments. If the amount you enter is the net amount you received after fees, the result is close to the APR; if you enter the face value of the loan and fees were charged separately, the true APR is higher than the rate shown. To estimate APR from a fee-bearing loan, subtract the fees from the amount borrowed and recalculate.
| Scenario | Enter as amount | Result |
|---|---|---|
| $10,000 loan, no fees, $212/month × 60 | $10,000 | 9.9% |
| Same, but a $500 origination fee deducted | $9,500 | 12.2% (this is the APR) |
| "0% finance" on $1,200 item, cash price $1,080, $100 × 12 | $1,080 | 20.2% |
Tips for accurate input
- Use the exact payment including cents; rounding $212.47 to $212 shifts the rate by a tenth of a point.
- Enter the number of payments, not years: 5 years of monthly payments is 60.
- If the payment does not cover the interest at any plausible rate (payment × n < amount), there is no valid solution — check the figures.
- For balloon or interest-only loans the formula does not apply; those need a cash-flow (IRR) calculation.