Already know your loan amount, term, and monthly payment, but not the rate? Enter those three and this calculator solves for the nominal annual interest rate, then shows the total of all payments, total interest, and a full amortization schedule for the rate it found. This is an implied note rate, not a lender-disclosed APR.
Worked example
| Input | Value |
|---|---|
| Loan amount | $32,000 |
| Term | 36 months |
| Monthly payment | $960 |
| Monthly rate (solved) | ≈ 0.422% |
| Nominal annual rate | ≈ 5.065% |
| Total of 36 payments | $34,560.00 |
| Total interest | $2,560.00 |
Examples
$32,000 loan, $960/month for 3 years
Repaying a $32,000 loan with 36 payments of $960 means paying back $34,560 in total — $2,560 of it interest. The rate that produces a $960 payment on $32,000 over 36 months is about 5.065% nominal annual interest (a monthly rate of about 0.422%).
Formula
The loan amount is the present value of the stream of level payments. For a monthly
rate r over n months and a payment PMT:
Loan = PMT × (1 − (1 + r)^−n) / r
There's no way to rearrange this for r, so the rate is found by numerical search
(bisection): try a rate, see whether it reproduces the loan amount, and narrow in.
The annual rate is then:
Nominal annual rate = r × 12
PMT × n, and the total
interest is that total minus the loan amount — independent of the exact rate.Interest rate versus APR
This solver has no fee input, so it cannot reproduce a disclosure APR when a loan has origination charges or other financed costs. The CFPB explains that APR combines the interest rate with additional loan fees. Use the contract's amount financed, finance charge, payment dates, and fees for a regulated APR comparison.