APR to APY calculator

APR, or annual percentage rate, is the yearly cost of borrowing, shown as a percent. It leaves out compounding. APY counts it, so it shows what a rate adds up to in a year. Enter either one to get the other, plus the daily rate and a year of interest. This tool converts rates. It does not add loan fees.

For credit cards, loans and savings rates · Free, no sign-up · How it works
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Use the APR on your statement or loan papers.

Compounds

Optional. Leave it empty to see the rates only.

The 20.00% APR you entered, compounded daily, is an APY of

22.13%
0.0548%Daily periodic rate (APR ÷ 365)
On $1,000, one year of interest with nothing paid and nothing added is $221. The balance would be $1,221.

Hypothetical illustration based on your inputs. Not a prediction, a recommendation, or the performance of any Amaltash strategy.

How it works: the rate you enter is compounded as often as you choose, for one year. Payments, new charges, fees and rate changes are not counted.

Results change each time you change an input.

Real rates change. Fees, taxes and penalties are not included, and a rate you are offered can differ from this one.

What is APR?

APR stands for annual percentage rate. It tells you, as one yearly percent, what a loan or a card charges you to borrow. A federal law, the Truth in Lending Act, says a lender must show you the APR before you sign.

APR is a yearly label, not the way interest is really billed. Lenders split it into small pieces and charge a piece each day or each month. Those pieces can stack on top of each other, which is why the true cost over a year can be more than the APR.

What is APY?

APY stands for annual percentage yield. It is a yearly rate with compounding counted in. Compounding means interest is added to the balance. Then that interest earns interest too.

Banks must show the APY on savings accounts and CDs, under the Truth in Savings rules. That lets you line up two accounts that add interest on different schedules. For example, a 3.9% rate that compounds daily has an APY of about 3.98%.

See what an APY earns on savings with the high-yield savings calculator →

APR vs APY: what is the difference?

APR and APY can describe the very same rate. APR skips compounding. APY shows what the rate adds up to in a full year, once interest earns, or charges, interest of its own. Here is one 12% APR, compounded four ways:

CompoundsTimes a yearAPY
Yearly112.00%
Quarterly412.55%
Monthly1212.68%
Daily36512.75%

Which label you see depends on the product. Lenders show APR, under the Truth in Lending rules. Banks show APY on savings accounts and CDs. So a loan and a savings account at the same rate can look different on paper.

How to convert APR to APY, and APY to APR

  1. Write the APR as a decimal. 6% is 0.06.
  2. Divide it by the number of times interest is added each year. For monthly, 0.06 ÷ 12 = 0.005.
  3. Add 1, then raise it to that same number. 1.005 to the 12th power is about 1.0617.
  4. Take away 1 and write it as a percent. That is a 6.17% APY.
APY=(1+APRn)n−1\text{APY} = \left(1 + \frac{\text{APR}}{n}\right)^{n} - 1

In words: Divide the APR by the times a year interest is added. Add 1. Write that number once for each time, and multiply them all together. Then take away 1.

APY\text{APY}
the yearly rate with compounding counted, as a decimal
APR\text{APR}
the yearly rate before compounding, as a decimal
nn
how many times a year interest is added

To go the other way, undo each step. A 5% APY that compounds monthly comes from an APR of about 4.89%.

APR=n[(1+APY)1/n−1]\text{APR} = n\left[\left(1 + \text{APY}\right)^{1/n} - 1\right]

In words: Add 1 to the APY. Take the root that matches the times a year. Take away 1. Then multiply by that same number.

APR\text{APR}
the yearly rate before compounding, as a decimal
APY\text{APY}
the yearly rate with compounding counted, as a decimal
nn
how many times a year interest is added

See a rate grow year by year with the compound interest calculator →

APY vs interest rate: why the APY is higher

The interest rate on a savings account works like an APR. It is the yearly rate before compounding. The APY adds compounding on top. So when interest is added more than once a year, the APY comes out a little higher.

For example, a 4.5% rate that compounds monthly has an APY of about 4.59%. If interest is added only once a year, the rate and the APY are the same.

Line up CD offers by APY with the CD calculator →

Effective annual rate (EAR)

The effective annual rate, or EAR, is the same math as APY under another name. Savers usually hear APY. Loans and finance classes often call it the EAR. You may also see it called the effective interest rate.

Take a loan at 18% APR that compounds monthly. Its EAR is about 19.56%. That is what the rate works out to over a year when each month's unpaid interest is added to the balance. This math adds compounding only. It does not add fees.

Why a loan's APR can be higher than its interest rate

On a loan, the interest rate is the price of the money alone. The APR adds some fees too. Under the Truth in Lending rules, points and loan fees count as finance charges. An origination fee, a charge for making the loan, is a common one. So a loan with these fees has an APR above its rate.

Here is a made-up example. You borrow $10,000 for 3 years at an 8% interest rate. The payment is $313.36 a month. Now say a $300 fee comes out of the loan, so you get $9,700. You repay the same amount, so the APR is about 10.08%.

This calculator does not add loan fees. It turns one form of a rate into another. For the full APR of a loan, fees and all, use the APR on the papers your lender must give you before you sign.

Cards work a little differently. A credit card states its interest rate as a yearly rate, and that rate is its APR. Card fees, like a yearly fee, are listed on their own.

Daily periodic rate

Many credit cards charge interest by the day. The card divides its APR by 365, or by 360 at some banks. The answer is the daily periodic rate.

daily rate=APR365\text{daily rate} = \frac{\text{APR}}{365}

In words: Divide the APR by 365, the days in a year. Some banks divide by 360 instead.

APR\text{APR}
the yearly rate before compounding, as a decimal
APRDaily rate (÷ 365)Daily rate (÷ 360)
12%0.0329%0.0333%
20%0.0548%0.0556%
30%0.0822%0.0833%

On a $1,000 balance at a 20% APR, one day of interest is about 55 cents.

Does credit card interest compound?

Yes, on many cards. They work out interest each day, using your average daily balance. Each day, the interest is added to what you owe. The next day, you pay interest on that interest too.

Here is an example with $3,000 at a 24% APR. It assumes no payments and no new charges, which a real card would not allow for long.

TimeInterest, added each daySimple interest
1 day$1.97$1.97
30 days$59.75$59.18
1 year$813.45$720.00

Left alone like this, the $3,000 would double in about 3 years. That is the rule of 72 at work: 72 ÷ 24 = 3.

Work out how fast a debt doubles with the rule of 72 calculator →

Credit card APR: the kinds you will see

One card can carry several APRs at once. The card's terms list each one:

  • Purchase APR: for things you buy with the card.
  • Balance transfer APR: for debt you move over from another card.
  • Cash advance APR: for cash you take out with the card.
  • Penalty APR: a higher rate that can start after a late payment.
  • Intro APR: a lower rate for a set time, sometimes 0%.

An APR can also be fixed or variable. A variable APR is tied to an index rate, so it moves when that index moves.

See how card debt counts against what you own with the net worth calculator →

How this calculator works

What it counts. One year of interest on the balance you enter, at a fixed rate, added as often as you pick.

What it leaves out. Payments, new charges, fees and rate changes. A real statement includes them.

The daily rate. We divide the APR by 365. If your card divides by 360, its daily rate is a bit higher.

Private. The math runs in your browser. Nothing you type is saved to an account.

Questions people ask

Is APR a monthly or a yearly rate?

It is a yearly rate, but it is charged in small steps. A 20% APR works out to about 0.0548% a day, or about 1.67% a month on a card that compounds monthly. Those small step rates are called periodic rates.

Does APR include compounding?

No. APR is the periodic rate times the number of periods in a year, so compounding is left out. APY, also called the effective annual rate, puts it back in. So the APY is higher whenever interest compounds more than once a year.

How can I avoid paying interest on a credit card?

Pay the full statement balance by the due date every month. On most cards, purchases then cost no interest at all. Carry part of the balance, and interest is charged on what is left.

What does a 0% intro APR mean?

For a set time, the balance covered by the offer is charged no interest. When that time ends, the regular APR applies to whatever is left. The card terms say how long it lasts and which balances it covers.

Should I compare offers by APR or APY?

Compare loans and cards by APR, the number lenders must show. Compare savings accounts and CDs by APY. If two offers use different labels, turn one into the other first with the same compounding.

Does this APR calculator include loan fees?

No. It turns a rate into another form of the same rate. It does not add points, origination fees or other loan costs. For the full APR of a loan, use the APR on the papers your lender must give you before you sign.

Is a lower APR always cheaper?

Not always. A lower APR costs less per year, but the length of the loan matters too. Pay a lower APR for many more years, and the total interest can be higher. Compare loans of the same length, or add up all the payments.

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Reviewed by Tavish Sharma, CFA · Last reviewed

Published by Amaltash Advisors LLC, an SEC-registered investment adviser

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