APR Calculator
Find the true cost of borrowing once fees are included, compare loan offers, and see how credit card interest and minimum payments really work — with clear supporting visuals.
Background
The interest rate on a loan and its APR (annual percentage rate) are often different numbers. The interest rate is just the cost of borrowing the principal. APR also folds in fees, points, and other upfront charges, spreading them across the loan term to show the true annualized cost — which is why a loan with a lower interest rate can sometimes have a higher APR than a competing loan with a slightly higher rate but far lower fees.
How to use this calculator
- Choose Loan APR for any borrowed lump sum repaid over time — a mortgage, auto loan, personal loan, or short-term loan. Use Installment for monthly-payment loans, or Single-payment for a loan repaid in one lump sum (like a payday or title loan), since the two use genuinely different APR formulas.
- Turn on Compare a second offer to weigh two versions of the same loan — classically, paying points upfront for a lower rate — and see the break-even point where the lower payment starts actually saving you money.
- Choose Credit Card for a revolving balance. Use Statement finance charge to see what one billing cycle actually costs, or Payoff simulator to see how long minimum payments really take compared to paying a fixed amount each month.
- Click Calculate to see the result, a supporting chart, and full step-by-step working.
How APR works
The note rate (or "interest rate") only prices the cost of the money itself. APR spreads fees and points across the loan term too, so it's almost always equal to or higher than the note rate.
The shorter the loan term, the more a fixed fee inflates the APR — because there's less time to spread that fee out. This is exactly why short-term loans with modest-looking flat fees can carry triple-digit APRs.
Buying points (prepaying interest for a lower rate) only pays off if you keep the loan past the break-even point — the month where accumulated monthly savings finally exceed what you paid upfront.
A credit card's APR is applied daily, not monthly — your daily periodic rate (APR ÷ 365) multiplies against your average daily balance, not just your statement balance on one date.
Minimum payments are often calculated as a small percentage of the current balance, so as the balance shrinks, so does the minimum payment — which is exactly why paying only the minimum can stretch a payoff out for decades.
Formula & Equations Used
Monthly payment: Payment = P × r / (1 − (1+r)^−n), where r is the monthly note rate and n is the number of months.
True APR (installment): the rate r that makes PV(Payment, r, n) = Amount Financed, where Amount Financed = Loan Amount − Fees.
Single-payment APR: APR = [Fee / (Loan − Fee)] × (365 / Days) × 100
Break-even on points: Months = Extra Upfront Cost / Monthly Savings
Credit card finance charge: Charge = Average Daily Balance × (APR/365) × Days in Cycle
Example Problems & Step-by-Step Solutions
These cover cases the Quick Examples chips above don't already demonstrate.
Example 1 — A zero-fee loan
A \)20,000 auto loan at 5% for 60 months has no fees at all. What's the APR?
Step: With no fees, Amount Financed equals the full loan amount, so the true APR calculation converges to exactly the note rate.
Result: APR = 5.00% — identical to the note rate, since there's nothing extra to spread across the term.
Example 2 — Comparing two short-term loans
Loan X: borrow \$500, pay a \$75 fee, repay in 21 days. Loan Y: borrow \$500, pay a \$60 fee, repay in 14 days. Which has the higher APR?
Step: Loan X: APR = [75/425] × (365/21) × 100 ≈ 307%. Loan Y: APR = [60/440] × (365/14) × 100 ≈ 355%.
Result: Loan Y has the higher APR (≈355% vs ≈307%) even though its dollar fee is smaller — because it has to be repaid in a much shorter window.
Example 3 — Finance charge from a lower balance
A card with an 18% APR carries an average daily balance of \$600 over a 31-day billing cycle. What's the finance charge?
Step: Daily periodic rate = 18%/365 ≈ 0.0493%. Finance charge = \$600 × 0.0493% × 31 ≈ \$9.17.
Result: Finance charge ≈ \$9.17 for that billing cycle.
Example 4 — Never quite paying it off
A \$2,000 balance at 26.99% APR is paid with a minimum of 3% of the balance (or \$30, whichever is greater). Why does this take so long to pay off?
Step: Monthly interest starts at \(2,000 × 26.99%/12 ≈ \)45. The first minimum payment (3% of \(2,000 = \)60) barely covers interest, and both interest and the required minimum shrink together as the balance drops.
Result: Because the payment is a percentage of a shrinking number chasing interest that's also shrinking, payoff can stretch on for many years — try it in the Payoff Simulator to see exactly how long.
Frequently Asked Questions
Why is APR higher than the interest rate on my loan estimate?
APR includes upfront fees and points spread across the loan term, while the interest rate only prices the principal itself. If your loan has any origination fees, discount points, or certain closing costs, APR will be higher than the quoted rate — sometimes only slightly, sometimes substantially, depending on the fee size and loan term.
Is a lower APR always the better deal?
Usually, but not always — APR assumes you keep the loan for its full term. If you plan to sell, refinance, or pay off a mortgage early, a loan with a lower APR but higher upfront points can actually cost more than a loan with a slightly higher APR and lower fees, since you never reach the points' break-even point.
Why do payday loans show such enormous APRs?
APR is an annualized rate, and payday loans are repaid in days, not years. A flat fee that looks modest in dollar terms translates into a huge annualized percentage once you stretch that same fee rate out over a full year — it's a real cost, just measured on a very different time scale than the fee itself suggests.
Does paying more than the minimum on a credit card actually make a big difference?
Yes, often dramatically — because minimum payments are typically a small percentage of the balance, a large share of each minimum payment goes toward interest rather than principal. Paying even a modest fixed amount above the minimum can cut years off the payoff time and save a significant amount in total interest.
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