APR calculator

An APR calculator for one loan. See the nominal APR and the effective annual rate once an upfront fee is included, next to the stated interest rate.

The figures are an estimate for learning, not a loan offer and not advice. See the disclaimer.

How this is calculated

This calculator finds the nominal APR and the effective annual rate once an upfront fee is included. The monthly payment repays the full principal over the term you enter in years and months. The APR is the rate that makes those payments equal the cash left after the fee. It is an estimate for learning, not a loan offer and not advice.

Formula

The monthly payment pays off the full principal over the term, at the stated nominal rate. The APR is the rate that makes those same payments worth the cash you actually receive after the fee.

Term n = 12 × years + months (1 to 600; months alone is allowed)

Fee = the amount you enter, or principal × (fee percent ÷ 100)

Net proceeds = principal − fee

Monthly rate r = stated annual rate ÷ 100 ÷ 12

Payment M = principal × r × (1 + r)^n ÷ ((1 + r)^n − 1). If r is 0, M = principal ÷ n

Nominal APR = 12 × the monthly rate that sets the present value of n payments of M equal to the net proceeds

Effective annual rate = ((1 + monthly APR rate)^12 − 1) × 100

Interest and fees = (M × n) − net proceeds

Assumptions

Payment on the full principal: Same formula as the mortgage calculator, on the amount you borrow — not on cash after the fee.
One upfront fee: Amount or percent of principal, taken off at the start. Not added to the balance; later fees excluded.
Term in years and months: n = 12 × years + months; months alone allowed; total 1–600. Daily/weekly payments not offered. For months to clear a revolving balance, or payment-from-term on one balance without fees, use the debt payoff calculator.
Stated rate: Zero stated rate → equal principal splits. APR stays above zero when a fee means you receive less than you repay.
Currency: Display only; no conversion.

Worked example

Borrow 12,000 at a stated 12% for 1 year 0 months (12 months) with no fee. Monthly payment 1,066.19; nominal APR 12%; effective annual rate about 12.68%. Borrow 10,000 at stated 0% for 0 years 10 months with a fee of 200: payment 1,000, you receive 9,800, nominal APR about 4.43%.

Inputs	Monthly payment	Nominal APR	Notes
12,000 @ 12%, 1 year 0 months, fee 0	1,066.19	12%	EAR ≈12.68%
10,000 @ 0%, 0 years 10 months, fee 200	1,000	≈4.43%	Net received 9,800

APR and the stated interest rate

The stated rate sets the monthly payment on the full amount you borrow. The APR is the rate on the cash you receive after the fee. With no fee, the two nominal rates match. With a fee, the APR is higher because you repay the full amount after receiving less.

FAQ

Why can the APR be higher than the stated rate?

The fee reduces the cash you receive. The payment still repays the full principal, so the rate on the smaller sum is higher.

What is the effective annual rate?

It compounds the monthly APR rate over 12 months. At a stated 12% with no fee, that effective rate is about 12.68%.

Does a zero fee make the APR equal the stated rate?

Yes for the nominal APR. The effective annual rate is higher whenever that rate is above zero, because of monthly compounding.

Is this the mortgage calculator?

No. Same monthly payment formula, then fee-inclusive APR. No mortgage schedule; mortgage page does not solve for a fee. For revolving payoff or term→payment without fees, use debt payoff.

What if the fee is as large as the loan?

The calculator stops. Zero cash after the fee means no rate matches a positive payment to zero proceeds.