APR Calculator

Interest rate vs. APR: the gap that costs borrowers

The interest rate on a loan tells you what the lender charges to borrow the money. The APR, or annual percentage rate, tells you what the loan costs you per year once fees are folded in. The two numbers look similar, but they answer different questions, and the gap between them is where borrowers lose money.

A loan can advertise a low interest rate and still cost more than a competitor with a higher rate, because the first loan tacks on an origination fee, points or closing costs. The APR adds those charges to the interest and spreads them across the life of the loan, so it is the single number you should compare when shopping. If you only look at the rate, you are comparing the sticker, not the price.

Two loans at 6% are not the same loan if one charges $800 up front and the other charges nothing. The APR makes that $800 visible as extra yearly cost. That is the whole point of the rule that requires lenders to show it. The law that requires the APR to appear next to the rate exists for exactly this reason: so a borrower can compare two offers on equal footing without doing the fee math themselves. The number does the comparison for you.

A worked example: $20,000 at 6% with an $800 fee

Take a $20,000 loan over 60 months at a 6% interest rate, with an $800 origination fee taken at signing. Here is what happens to your money.

• The monthly payment is fixed by the 6% rate: $386.66.
• You make 60 payments, so the total of payments is $23,199.36.
• Subtract the $20,000 you borrowed and the interest comes to $3,199.36.
• Add the $800 fee and the loan costs $23,999.36 all in.
• Because you only received $19,200 after the fee, the rate that matches those payments to what you got is 7.71%, not 6%.

So the advertised 6% becomes a 7.71% APR. The fee did not change your monthly payment, but it changed the price of the loan by 1.71 percentage points. That is the number a loan officer may not lead with, and the number this calculator puts first.

How the calculator solves for the true APR

The math behind APR is a present value problem, and you can understand it without formulas. Your monthly payment is worked out from the advertised interest rate on the full loan amount. The calculator then asks a second question: what yearly rate would make those exact payments worth only the cash you received, after the fee came out?

If you borrow $20,000 and hand $800 back as a fee, you received $19,200. The lender still collects $386.66 a month for 60 months. The rate that makes 60 payments of $386.66 equal $19,200 today is the APR. The tool solves for that rate by narrowing in on it, the same way you would guess a temperature and adjust until the math balances.

The result is exact to two decimal places for any combination of amount, term, rate and fee you enter. When the fee is zero, the APR equals the interest rate, which is the sanity check that the calculation is right.

Same loan, different fees: a side-by-side comparison

The same loan, different fees, different answers. Each row below uses level monthly payments and a single upfront fee:

Read the first two rows together: same loan, same payment, and the fee alone lifts the APR from 5.00% to 7.05%. A $300 fee on a small loan is a bigger percentage hit than a $1,500 fee on a large one, because the fee is measured against what you borrow. Shorter terms also feel the fee more, since there are fewer payments to spread it across.

Where the cost hides: fees that quietly raise your APR

Lenders lead with the interest rate because it is the smaller, friendlier number. The fee is the part they tuck into the paperwork. Three places this shows up most:

• Origination fees. A 1% to 2% fee on the loan amount is common on personal and auto loans, and it shows up almost entirely as a higher APR rather than a higher payment.
• Discount points on a mortgage. You pay upfront to buy a lower rate. The points raise the APR even as the rate falls, so a no points loan can have the better APR despite the higher rate.
• Cash advance and payday style products. A flat fee plus a short term produces an APR in the triple digits, which is why a small fee can look enormous once it is annualized.

The Consumer Financial Protection Bureau explains the difference between a rate and an APR in plain terms, and its loan estimate form is built to put the APR next to the rate so the gap is impossible to miss. Always read the APR line before you sign.

What APR leaves out: its limits as a single number

APR is a useful single number, but it is not the complete cost of borrowing, and knowing its edges keeps you from over trusting it.

• It includes: the interest rate, origination fees, discount points and some closing costs, all spread across the loan term.
• It excludes: property taxes, homeowner insurance, late fees, and the effect of a balloon payment or a rate that changes after a teaser period.
• Mortgage APR can differ by regulation from credit card APR, because the set of included fees is not identical across loan types.

For a credit card the APR is the interest rate plus little else, so the card APR and the card rate are nearly the same number. For a mortgage the included fees can move the APR by a full point or more. The Federal Reserve publishes average rates across loan types, which is a handy way to tell whether the APR you are offered is typical or padded.

This calculator is an estimate from the numbers you enter, not financial advice. Real loan paperwork uses your exact fee schedule and payment timing, so confirm the final APR with the lender before you commit.

APR vs. APY: why daily compounding hides the real rate

APR measures the cost of borrowing, but a credit card also compounds interest every day you carry a balance. The rate that applies to revolving debt is the APY, or annual percentage yield, which bakes daily compounding into the number. The gap between APR and APY widens as the rate climbs.

A card advertised at 25% APR costs closer to 28% once daily compounding lands on a balance that is not paid off, because each day charges interest on the prior day interest. Pay the balance in full and compounding never starts, so the APR and the real cost line up.

Two offers, one APR rule: how to pick the cheaper loan

When two loans show different rates and fees, the lower rate is not always the cheaper loan. Run each offer through the APR rule, which folds the fee into the rate, and the order can flip.

Offer B charges a higher rate but no fee, so its APR is the rate itself. Offer A hides $800 in fees that push its APR above B even though its rate is half a point lower. Offer C shortens the term and drops the rate, and the fee barely moves the APR. The calculator shows the APR so you compare the true yearly cost, not the headline number.