APR Calculator
Estimate a fee-adjusted annual loan rate from net funds received and equal monthly repayments.
Estimated nominal annual APR
Estimate only, not an official lender APR. Equal payments at month end, first payment after one month, fees paid upfront from proceeds, no irregular dates, financed fees, insurance or variable rates. Jurisdiction and lender methodology may differ.
Formula checked · NumberSwift · Review process
For informational purposes only. Results are estimates and do not constitute financial advice.
How this calculator works
First calculate equal monthly payments using principal and the nominal annual rate divided by twelve. Subtract upfront fees from the principal to model the net amount received. Solve for the monthly discount rate at which the present value of those payments equals net proceeds. Multiplying that solved monthly rate by twelve produces the nominal annual estimate shown here. Different statutory APR conventions, timing rules and fee definitions can produce different disclosures.
Formula
Net proceeds = principal − upfront fees. Solve net proceeds = Σ(payment/(1+i)^m), m=1…term months. Estimated nominal annual APR (%) = monthly solved rate i × 12 × 100.
Assumptions & limitations
Estimate only, not an official lender APR. Equal payments at month end, first payment after one month, fees paid upfront from proceeds, no irregular dates, financed fees, insurance or variable rates. Jurisdiction and lender methodology may differ.
Sources & reference material
- OpenStax: annuities ↗
Background for equal-period cash flows; not a forecast of returns or a lender APR disclosure.
Worked example
A 1,200 loan at 0% nominal interest for 12 months has 100 monthly payments. A 100 upfront fee leaves 1,100 net proceeds. Solving 1,100 = Σ(100/(1+i)^m) gives an estimated nominal annual APR of about 16.38%; this is higher than the nominal 0% rate.
Our approach to calculations ↗Common questions
Is this the APR a lender must disclose?
No. It is an explicit equal-month cash-flow estimate. Disclosure rules differ by jurisdiction, product, included fees and timing.
Where should financed fees go?
This tool assumes entered fees reduce upfront proceeds while repayments use the stated principal. Financed fees need a different cash-flow setup; do not enter them as if paid from proceeds.
Why does APR increase when the nominal rate stays the same?
Upfront fees reduce what you receive without reducing scheduled repayments, raising the cash-flow cost.
What happens when fees are zero?
Under this tool’s equal-month nominal convention, the estimate equals the entered nominal annual rate.