APR calculator
See the true APR of a loan offer including origination fees and other charges. Or work backwards from a quoted payment amount to verify the APR your lender has disclosed.
Deducted from the loan proceeds at signing
How does this APR calculator work?
An APR calculator computes the true annualized cost of credit by combining the interest rate with fees that are part of the cost of borrowing. For a $2,000 loan at a stated 25% interest rate over 12 months with a $50 origination fee, the true APR is approximately 30.4% — higher than the stated rate because the fee reduces what you actually receive while you still repay the full loan amount.
Why APR matters more than interest rate
If two lenders both quote you a 25% interest rate, you might assume they're equivalent offers. They're often not. One might charge a $50 origination fee deducted at signing; the other might not. The first loan has a true APR around 30%; the second has an APR of 25%. Same headline rate, very different actual cost.
Federal law (Truth in Lending Act, Regulation Z) requires lenders to disclose APR specifically because of this — interest rate alone hides the impact of fees. The APR figure exists to give borrowers an apples-to-apples comparison number that accounts for the full cost of credit.
The two modes of this calculator
Mode 1: Forward calculation
You have a stated interest rate, you know the loan amount and term, and you want to see what the APR is once fees are included. Enter the four inputs and the calculator shows you the true APR plus the gap between the stated rate and the actual cost.
Mode 2: Reverse calculation
You have a loan offer with a monthly payment amount but the APR isn't displayed prominently (or you want to verify it). Enter the loan amount, the monthly payment, the number of payments, and any fees deducted at signing. The calculator back-solves for the APR using the same formula regulators use.
Mode 2 is the rare and useful one. Most online calculators only do mode 1. If you've ever wanted to confirm a lender's disclosed APR matches the actual cash flow, mode 2 is the math you'd otherwise need to do by hand.
What APR includes and excludes
Included in APR (per Regulation Z):
- The interest rate itself
- Origination fees and processing fees
- Document fees and prepaid finance charges
- Mandatory credit insurance premiums (if any)
Excluded from APR:
- Late payment fees (because you might not pay one)
- NSF or returned-payment fees
- Early payoff penalties (rare on personal loans)
- Optional add-ons like credit insurance you choose to add
The math behind the back-calculation
Reverse APR calculation requires solving for the rate that makes the present value of all future payments equal the amount actually received. There's no closed-form solution — it requires iterative numerical methods. This calculator uses Newton-Raphson iteration, the same technique financial calculators use, and converges to within 0.01% of the true rate in a few iterations.
If you want to verify a lender's disclosed APR, enter the loan amount, payment, term, and any signing fees from their loan agreement. The calculator should produce a number within a few hundredths of a percent of the disclosed APR. If there's a meaningful gap, the disclosure may be incorrect — worth checking.
Related calculators and guides
Frequently asked questions
What's the difference between APR and interest rate?
The interest rate is the cost of borrowing the principal as a percentage. APR includes that interest rate plus most fees expressed as an annualized percentage. APR is almost always equal to or higher than the interest rate. By federal law (Regulation Z), lenders must disclose APR before you sign — but knowing how to back-calculate it from actual cash flows lets you verify their number.
Why would I want to back-calculate APR?
Two reasons. First, to verify the APR your lender has disclosed matches the actual payment schedule. Second, to compare offers when one lender gives you a payment amount but doesn't prominently display the APR. The reverse-calculation mode of this calculator takes the loan amount, monthly payment, and term, and produces the true APR.
Are origination fees always part of APR?
Yes. Origination fees, document fees, and processing fees are all required to be included in the APR calculation under Regulation Z. The exception is fees that depend on borrower behavior — late fees, NSF fees, and early payoff fees aren't included because you might never pay them.
How accurate is the reverse APR calculation?
The calculator uses Newton-Raphson iteration to solve for the rate that satisfies the cash flow equation. It typically converges to within 0.01% of the true APR within a few iterations. For typical loan structures, the result matches what a regulator-approved APR calculator would produce.
Can a loan have an APR lower than the interest rate?
Almost never on consumer loans. The only common case is when a lender pays your closing costs at signing in exchange for a slightly higher rate — common in mortgages, rare in personal loans. If you see an APR significantly lower than the stated interest rate on a personal loan offer, ask the lender to explain. Something unusual is happening.
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