APR Calculator: Nominal, Effective & True APR

Nominal ↔ effective APR

Convert a quoted rate across compounding frequencies, including continuous.

%

Quoted annual rate, 0–25

Compounding frequency

True APR with fees

Add upfront fees to see the real annual cost — the rate that equates your payments to the cash you actually receive.

$

Full borrowed amount before fees

$

Origination, points, closing — taken from proceeds

%

Quoted note rate, 0–25

Repayment period, 1–360

Compare two offers

Same loan, different fine print — the lower true APR wins, even when the nominal rate says otherwise.

Offer A

Offer BLower true APR wins

Δ 1.979 pp — Lower true APR wins

True APR

9.479%

Effective APR: 6.168%

Monthly payment
$304.22
Effective APR
9.902%
Total paid
$10,951.92
Total cost of credit
$1,451.92

Lower true APR wins — Δ 1.979 pp

APR Calculator — Quoted Rate, Real Cost, Better Offer

A 6% loan with $500 in fees is not a 6% loan — its true cost is 9.479% a year. This free calculator works three jobs: convert nominal rates across compounding frequencies (yearly to continuous), reveal the fee-inclusive true APR behind any quoted note rate, and compare two loan offers head-to-head so the lower true APR wins even when the nominal rate says otherwise.

Enter any rate with any frequency for instant conversion, add upfront fees to expose the real annual cost with payment and total cost, then pit two offers against each other. Every calculation runs locally in your browser with no sign-up, and any scenario can be shared with a link.

The APR formulas

effective=(1+nominaln)n−1\text{effective} = \left(1 + \frac{\text{nominal}}{n}\right)^{n} - 1
effectivecont=enominal−1\text{effective}_{\text{cont}} = e^{\text{nominal}} - 1
payment=P r(1+r)n(1+r)n−1\text{payment} = \frac{P\,r(1+r)^{n}}{(1+r)^{n} - 1}
APR=IRRmonthly×12\text{APR} = \text{IRR}_{\text{monthly}} \times 12

Effective APR compounds the nominal rate at the stated frequency; continuous compounding uses the exponential instead. True APR is the monthly internal rate of return on your actual cashflows — payments out versus cash received — annualized the Truth-in-Lending way, times twelve.

Payment uses the standard amortization formula.

How it works

  1. Pick a direction and frequency, enter a rate, read the converted APR instantly.
  2. Enter amount, fees, note rate and term to reveal true APR with payment, effective APR and total cost.
  3. Enter two offers; the lower true APR wins with the delta shown — ties and unsolvable legs explained.

True APR equates payments to cash received

Borrow $10,000 with $500 in fees at 6% over 36 months and you receive $9,500 while paying $304.22 a month — the rate equating those flows is 9.479%. With zero fees the true APR equals the note rate exactly.

What v1 leaves out

No amortization tables, no tax treatment, no variable rates — conversion plus true APR plus comparison only. Follow-ups add schedules and adjustable-rate views.

Frequently asked questions

Why is APR higher than my note rate?

Fees. You pay interest on money you never received, so the true annual cost exceeds the quoted rate — $500 in fees on the worked example lifts 6% to 9.479%.

Nominal vs effective vs true APR?

Nominal is the quoted rate; effective compounds it at the stated frequency; true APR folds upfront fees into a monthly internal rate of return. Compare loans on true APR.

Which fees sit inside APR?

Upfront lender charges taken from proceeds: origination, points, closing costs. Enter their total in the fees field; anything paid separately stays outside.

How does comparison pick the winner?

Each offer's true APR is computed independently and the lower one wins, with the delta in percentage points. Equal within 0.0005 is a tie; unsolvable offers lose by default.

How accurate is the true APR?

The Newton-Raphson solver converges to twelve decimal places on the monthly rate before annualizing, verified against reference vectors to the thousandth. Extreme inputs fall back to bisection, then report unsolvable rather than guessing.