Interest Rate Finder
Find the implied interest rate when you know the present value, future value, and number of periods.
Reverse-engineer any growth rate.
Reverse interest rate calculation solves for the unknown interest rate when you already know the loan amount, payment amount, and loan term. This is useful when you receive a financing offer and want to verify the actual APR — lenders sometimes quote a monthly rate or omit fees that affect the true cost.
The loan payment formula (standard amortization):
PMT = P × [r(1+r)ⁿ] ÷ [(1+r)ⁿ − 1]
Variable definitions:
- PMT = regular payment amount (monthly, weekly, etc.)
- P = principal (loan amount)
- r = periodic interest rate (annual rate ÷ 12 for monthly)
- n = total number of payments
Solving for r: There is no closed-form algebraic solution — this equation must be solved numerically. The calculator uses the Newton-Raphson iterative method, which converges to the answer in typically 10–20 iterations to 8+ decimal places of precision.
Worked example: You are offered financing on a $25,000 car loan. The dealer says the payment is $487/month for 60 months. What is the actual APR?
- P = $25,000, PMT = $487, n = 60
- Total paid: $487 × 60 = $29,220
- Total interest: $29,220 − $25,000 = $4,220
- Solving iteratively: r ≈ 0.005983/month → APR ≈ 7.18%
Compare that to the advertised rate — if the dealer said “low financing,” you now know the real number.
APR vs. nominal rate:
- Nominal rate = the stated annual rate, compounded monthly
- APR (Annual Percentage Rate) = nominal rate plus fees, spread over the loan term
- APY (Annual Percentage Yield) = the effective annual rate including compounding
Why this matters: Knowing the implied interest rate lets you:
- Compare competing loan offers on an equal footing
- Detect whether fees have been rolled into a loan
- Decide whether to pay cash, finance, or refinance