APR Calculator

Two loans with the same interest rate can cost very different amounts once fees are added. APR folds the interest and the upfront fees into a single rate, which is why it — not the note rate — is the honest basis for comparing offers. This calculator finds it.

What is APR (annual percentage rate)?

APR — annual percentage rate — is the cost of borrowing expressed as a single yearly rate that includes both the interest and most upfront fees charged to obtain the loan: origination fees, points, and similar lender charges. It exists because the interest rate alone is gameable: a lender can advertise a low rate while recovering the difference in fees, and a borrower comparing rates would pick the worse loan. US lending law (the Truth in Lending Act) therefore requires lenders to disclose an APR for mortgages, auto loans, personal loans, and credit cards, computed by a standardized method.

The intuition is simple: fees mean you receive less than the loan amount, but you make payments as if you received all of it. If you 'borrow $10,000' but $350 in fees comes off the top, you have use of $9,650 while paying interest on $10,000. Your effective rate — the APR — is therefore higher than the note rate. The shorter the loan, the harder fees bite, because the same fee is spread over fewer payments; a $350 fee adds far more to the APR of a 12-month loan than of a 60-month loan.

APR is not perfect. It assumes you keep the loan for its full term — pay it off or refinance early and the fee is spread over fewer payments, making your true effective rate higher than the disclosed APR. Some fees are also excluded from the official calculation (certain third-party and conditional charges), so APRs from different lenders should be compared alongside the itemized fee sheets. Even with those limits, it is far better than comparing note rates, and it is the number this calculator reproduces from any offer's raw ingredients.

How APR (annual percentage rate) is calculated

There is no closed-form formula for APR; it is found by solving an equation. First the calculator computes the monthly payment from the note rate on the full loan amount. Then it asks: at what monthly rate would that exact stream of payments be worth exactly the net amount you receive after fees? That rate, found here by bisection — repeatedly halving an interval until the present value of the payments matches the net proceeds to the cent — is multiplied by 12 to give the APR.

This mirrors the regulatory method for closed-end credit, where the APR is the rate that equates the present value of the payment stream with the amount financed. Prepaid finance charges reduce the amount financed; that is the only role fees play, and it is why rolled-in fees (added to the balance instead of deducted) produce a slightly different figure — in that case, enter the fee in this calculator as if deducted, and increase the loan amount by the fee, to approximate the same economics.

The practical shopping rule: when two offers differ in both rate and fees, do not compare either number alone — compare APR, and also compare total cost of credit (interest plus fees) if you expect to keep the loan for its full term. A lower rate with high fees wins on a long loan and loses on a short one; APR captures that trade-off in one figure, and this calculator lets you test an offer in seconds.

For mortgages, remember that the disclosed APR also bakes in mortgage insurance and certain closing costs, and that it assumes the full 30-year term — very few borrowers keep a loan that long, so their effective rate ends up higher than the APR suggests. The direction is still right for comparisons between simultaneous offers.

Worked example

You borrow $10,000 at a 7% note rate for 36 months, with $350 of upfront fees. The note rate says 7% — the APR says otherwise. The calculator is pre-loaded with this offer.

The $350 fee lifts the true cost from 7.00% to about 9.42% APR — as if the rate were nearly two and a half percentage points higher with no fees at all. That is not an argument that the loan is bad; it is an argument for comparing it against, say, a 7.4% loan with no fees, which many borrowers would reflexively reject as 'more expensive' while actually paying less.

Shorten the same offer to 12 months and the APR climbs to about 13.7%: the identical fee is now recovered over twelve payments instead of thirty-six. This is why payday-style and short-term credit with fixed fees carries such extreme APRs, and why fee-heavy offers should always be evaluated at the term you truly expect to hold.

APR on credit cards works differently

For revolving credit there are no fixed payments to solve for, so a card's APR is simply its interest rate expressed annually — the daily periodic rate times 365. It excludes some charges (annual fees, penalty fees are disclosed separately), which is why a card with a lower APR but a hefty annual fee can cost a light user more than a higher-APR, no-fee card. Card APRs also come in flavors — purchase, cash advance (higher, no grace period), balance transfer, and penalty APR — each applying to its own balance bucket.

Because card interest is charged on an average daily balance, the practical question is rarely the APR formula but the payoff math: a fixed payment against a card balance. That is the loan payoff calculator's job — enter the balance, the APR, and the payment you can sustain.

APR vs. interest rate vs. APY — keeping the three straight

Interest rate is the bare cost of the money before fees. APR is the borrower's comparison rate: interest plus prepaid fees, annualized. APY runs the other direction — it is the saver's rate, expressing what a deposit earns in a year including compounding. A loan advertises APR; a savings account advertises APY; both exist so that compounding and fees cannot be hidden, one on each side of the bank's desk.

One asymmetry trips people up: APR does not compound — it is the monthly solving rate times 12, by law. APY does compound. So a 12% APR loan and a 12% APY savings account are not mirror images, and converting between conventions requires the APY calculator's formula rather than simple multiplication.

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