Reference formulas and worked examples below keep their stated units. Monetary examples use USD; dimensional examples use US customary units unless labeled otherwise. Metric calculator inputs are converted to these reference units before calculation. Choosing another currency does not convert example amounts or exchange money.
How to use this apr calculator
Choose known cash flows or build them from a loan rate and fees. This is a monthly IRR estimate, not a jurisdiction-specific legal APR disclosure.
How the calculation works
Treat the net amount received at month 0 as a positive borrower cash flow, followed by negative monthly payments. Solve for monthly rate r such that net proceeds = sum of payment at month t ÷ (1 + r)^t.
Estimated nominal annualized rate = 12 × r × 100%. Effective annual cost = [(1 + r)^12 − 1] × 100%. This distinction is separate from deposit APY and from local legal fee-inclusion and timing rules.
Known-cash-flow mode uses exactly the equal payments entered. Loan-and-fees mode uses monthly interest from the nominal annual loan rate and cent-rounded amortization, including a final adjusted payment.
With cash-paid or deducted fees, net proceeds are loan amount minus fees and principal stays unchanged. With financed fees, net proceeds stay at the base loan amount while principal includes the fees. A log-rate bisection solves the cash flows without assuming the nominal loan rate is the answer.
Worked example
Receiving 1,200 and repaying 100 at the end of each of 12 months gives a 0% cash-flow rate. Deducting a 100 fee while keeping those payments changes net proceeds to 1,100 and produces a positive borrowing rate. For a one-month example, receiving 1,000 and paying 1,100 gives a 10% monthly rate, a 120% nominal annualized estimate, and about 213.84% effective annual cost.
Limits and assumptions
Regular monthly timing only. It does not implement every legal APR rule, required fee category, day-count basis, odd first period, balloon, multiple disbursement, deferred installment, contingent charge or national disclosure convention. Negative rates can occur mathematically if repayments total less than proceeds; they do not certify a financial product. Compare the lender’s official disclosure separately.
Frequently asked questions
Is the displayed estimate a legal APR disclosure?
No. It is an annualized monthly cash-flow IRR under the inputs and timing shown. Statutory APR can depend on required fees, date conventions and jurisdiction.
Why can fees make the rate higher than the loan interest rate?
You receive less usable money, or repay a larger financed amount, while still making the modeled payments. The cash-flow rate reflects that difference.
Why show an effective annual cost as well?
Multiplying a monthly rate by 12 gives a nominal annualized figure. Compounding the same monthly rate for 12 months gives a different effective figure. Neither is a guaranteed investment return.
Does a zero interest loan always have a zero estimated APR?
No. Fees can make its net-proceeds cash-flow rate positive. Zero applies when the scheduled repayments equal the net amount received under this simple timing model.
How is the final payment handled?
Cash-flow mode uses identical payments. Loan mode clears cent rounding in its final payment; the IRR uses those actual modeled payments.
References
CFPB: actuarial APR computations and regulated timing conventions