Summary
Use APR when comparing offers that differ in fees: the nominal rate alone can understate borrowing cost if you pay points or origination fees upfront.
Calculation details
The regular payment is calculated from the face amount and nominal rate. A numerical monthly internal-rate-of-return solution equates net proceeds after fees with future payments, then compounds that rate annually. A higher effective APR than the nominal rate usually means fees meaningfully raised the cost of funds.
Formula
Net proceeds = loan amount − fees. Solve net proceeds = Σ payment ÷ (1 + monthly IRR)^t, then effective APR = [(1 + monthly IRR)^12 − 1] × 100.
Worked example
$20,000 loan with a $500 fee
A five-year loan at a 7% nominal rate has a higher effective APR once the borrower receives only $19,500 in net proceeds.
How it works
Enter face loan amount, nominal annual rate, term, and fees paid upfront. The solver uses a bounded binary search and reports an error if a valid solution cannot converge.
Frequently asked questions
What does this APR estimate include?
It includes the nominal rate and upfront fees entered, using net borrower proceeds.
When is this APR most useful?
When comparing loans that advertise similar rates but different upfront fees.
Are displayed values rounded?
The formula keeps full numeric precision. Values are rounded only when formatted for display.
Can actual results differ?
Yes. Fee timing, compounding conventions, and lender-specific APR rules can differ from this educational IRR-style estimate.