Loan Interest Rate Calculator
Find the interest rate of a loan from the amount borrowed, the monthly payment and the number of payments — the annual rate, the monthly rate, the effective annual rate and the rate including upfront fees.
How it works
Solve for i in P = A × [1 − (1 + i)⁻ⁿ] ÷ i (numerically) · annual rate = 12 × i · EAR = (1 + i)¹² − 1 · rate with fees: same equation with P − fees
There is no closed-form formula for the rate of an amortizing loan, so the calculator searches for the monthly rate at which the present value of all the payments equals the money you receive — the same internal-rate-of-return method regulators use for APR, TAE and CAT disclosures. Useful when a store, dealer or lender only tells you the payment. Adding the upfront fees shrinks the money you really receive and raises the rate.
Worked example
Borrowing 20,000 and repaying 450 a month for 60 months means 27,000 repaid and 7,000 of interest. The monthly rate that discounts those 60 payments back to 20,000 is 1.042%, so the annual interest rate is 12.50% (13.25% effective). With no fees the APR is the same 12.50%; an opening fee would push it higher.
Sources: Wikipedia — Mortgage calculator (annuity formula) · Wikipedia — Annual percentage rate
Frequently asked questions
How do I find the interest rate if I only know the payment?
Enter the amount you borrow, the payment and how many payments there are. The rate that makes those payments repay exactly that amount is the loan’s interest rate.
Why is the rate with fees higher?
Fees reduce the money you actually get while the payments stay the same, so the effective cost of borrowing rises. That is the idea behind APR (US), TAE (Spain) and CAT (Mexico).
What is the difference between the nominal and effective annual rate?
The nominal rate is 12 × the monthly rate. The effective annual rate compounds the monthly rate over 12 months and is always a little higher.
Can the rate come out at 0%?
Yes — if the payments add up exactly to the amount borrowed, as with a true “interest-free” installment plan.
Related calculators
Estimates for education and planning, not financial advice. Lenders’ contracts, fees, day-count and rounding rules differ — check the official cost disclosure (APR / TAE / CAT) in your loan or card agreement before deciding.