APY calculator

Turn an interest rate into an APY, or an APY back into the interest rate behind it, for any compounding frequency. Then see what that APY pays in dollars on your balance.

What do you want to convert?
4% is an example for the maths, not a rate on offer today. Use the figure from your own account.
For part of a year, use a decimal. Six months is 0.5.
APY conversionDaily compounding
APY (annual percentage yield)
4.08%

On $10,000.00 that is $408.08 of interest in a year, which is $8.08 more than the interest rate alone suggests.

Daily4.08%APY$408.08 a yearYour choice
Monthly4.07%APY$407.42 a year
Yearly4.00%APY$400.00 a year
Interest rate
4.000%
Rate applied each time (daily)
0.0110%
Added by compounding
+0.081%
APY
4.081%
Starting balance
$10,000.00
Interest in the first year
$408.08
Interest over 1 year
$408.08
Balance after 1 year
$10,408.08

Estimate only. The dollar figures assume the rate stays the same, nothing is added or taken out, and no fees or tax are deducted. Banks round the APY they advertise to two decimal places.

CheckMySum. Printed . This is an estimate, not tax, legal or financial advice.

Short answer: APY is the interest rate with compounding included. The formula is APY = (1 + r/n)^n − 1, where r is the interest rate and n is the number of times interest is compounded each year. A 4% rate compounded daily is an APY of 4.08%, which pays $408.08 a year on $10,000.

Check the APY earned on a statement

Type in three figures from a bank statement to see the APY your money earned in that period. This is a separate sum from the conversion at the top of the page.

The starting numbers are an example. Use the figures printed on your own statement.
APY earned check31 days
APY earned
4.01%

$33.42 on an average balance of $10,000.00 over 31 days works out at this yearly rate. Compare it with the APY the bank advertises.

Interest ÷ average daily balance
0.3342%
Raised to the power of 365 ÷ days
11.774
APY earned
4.01%

This is the Regulation DD formula for the APY earned on a periodic statement: 100 × [(1 + interest ÷ average daily balance)^(365 ÷ days) − 1]. It is an estimate of what your bank would print. A short period with rounded interest can move the answer by a few hundredths of a point.

CheckMySum. Printed . This is an estimate, not tax, legal or financial advice.

How APY is calculated

APY stands for annual percentage yield. It answers one question: by what percentage does a balance grow in a year if the interest is left in the account?

  1. Interest rate to APY. Write the rate as a decimal (r) and count the compounding periods in a year (n).
    APY = (1 + r/n)^n − 1
    For 4% compounded daily: (1 + 0.04 ÷ 365)^365 − 1 = 4.081%.
  2. APY to interest rate. This is the same formula turned round.
    r = n × ((1 + APY)^(1/n) − 1)
    An APY of 4.00% with daily compounding comes from an interest rate of 3.922%.
  3. APY to dollars. Because the APY already includes compounding, the dollar sum does not need the frequency.
    Interest = balance × ((1 + APY)^years − 1)

The federal rule for banks, Regulation DD, writes the formula a different way. It starts from the dollars of interest an account pays.

APY = 100 × [(1 + interest ÷ principal)^(365 ÷ days in term) − 1]

The regulation gives this example: an account that pays $61.68 of interest on $1,000 over 365 days has an APY of 6.17%. Both versions give the same answer. One starts from the rate, the other from the interest paid.

Worked examples

The rates here are picked to show the maths. They are not rates any bank is offering.

A 4.5% interest rate compounded daily

You know the interest rate and want the APY, then the dollars on $15,000 over one year.

  • Interest rate4.500%
  • CompoundingDaily
  • APY4.602%
  • Interest in the first year$690.37
  • Interest over 1 year$690.37
  • Balance after 1 year$15,690.37

A 5.00% APY with monthly compounding

You know the APY and want the interest rate behind it, then the dollars on $8,000 over three years.

  • Interest rate4.889%
  • CompoundingMonthly
  • APY5.000%
  • Interest in the first year$400.00
  • Interest over 3 years$1,261.00
  • Balance after 3 years$9,261.00

A 3% interest rate compounded quarterly, held for six months

$2,500 for half a year. The time is entered as 0.5 years.

  • Interest rate3.000%
  • CompoundingQuarterly
  • APY3.034%
  • Interest in the first year$75.85
  • Interest over 0.5 years$37.64
  • Balance after 0.5 years$2,537.64

APY table for interest rates from 1% to 6%

Find the interest rate in the first column, then read across to the compounding frequency.

APY to three decimal places. Banks show APY to two. The rates are a reference range, not current market rates.
Interest rateDailyMonthlyQuarterlyYearly
1.00%1.005%1.005%1.004%1.000%
1.50%1.511%1.510%1.508%1.500%
2.00%2.020%2.018%2.015%2.000%
2.50%2.531%2.529%2.524%2.500%
3.00%3.045%3.042%3.034%3.000%
3.50%3.562%3.557%3.546%3.500%
4.00%4.081%4.074%4.060%4.000%
4.50%4.602%4.594%4.577%4.500%
5.00%5.127%5.116%5.095%5.000%
5.50%5.654%5.641%5.614%5.500%
6.00%6.183%6.168%6.136%6.000%

Two things stand out. Yearly compounding leaves the rate unchanged. And the step from monthly to daily is small at every rate in the table, while the step from yearly to monthly is roughly ten times larger. At a 4% interest rate, daily compounding gives 4.081% and monthly gives 4.074%, a difference of about $0.67 a year on $10,000.

APY, APR and interest rate

These three terms are often used as if they mean the same thing. They do not.

  • Interest rate. Regulation DD defines it as the annual rate of interest paid on an account which does not reflect compounding. It is the r in the formula.
  • APY. The same regulation defines it as a percentage rate reflecting the total amount of interest paid on an account, based on the interest rate and the frequency of compounding for a 365-day period. It is what you earn.
  • APR. Annual percentage rate is the term used for borrowing. For credit cards, the Consumer Financial Protection Bureau describes it as the interest rate stated as a yearly rate. It is what you pay.

The practical rule: compare savings accounts and CDs by APY, because two accounts with the same interest rate and different compounding pay different amounts. Use the interest rate when a formula or another calculator asks for the rate before compounding.

What banks must tell you

The Truth in Savings Act of 1991 is carried out through Regulation DD. Its stated purpose is to enable consumers to make informed decisions about accounts at depository institutions. Under it:

  • Account disclosures must give the annual percentage yield and the interest rate, using those terms, and say how often interest is compounded and credited.
  • An advertisement that states a rate of return must state it as an annual percentage yield. The interest rate may be shown too, but not more prominently than the APY.
  • An advertisement that states an APY must also give the minimum balance needed to earn it and say that fees could reduce the earnings. For a variable-rate account it must say that the rate may change after the account is opened.
  • The APY and the interest rate are rounded to the nearest one-hundredth of a percentage point and shown to two decimal places. A disclosed APY counts as accurate if it is within 0.05 of a percentage point of the calculated figure.

Regulation DD applies to banks and other depository institutions except credit unions. Credit unions come under a separate National Credit Union Administration rule that carries out the same act.

APY earned on your statement

A statement may show a figure called APY earned. It uses the second formula above with real numbers: the interest actually paid in the statement period, your average daily balance, and the number of days in the period.

APY earned = 100 × [(1 + interest earned ÷ average daily balance)^(365 ÷ days in period) − 1]

Take a 31-day statement that shows $33.42 of interest on an average daily balance of $10,000.00. The interest is 0.3342% of the balance. Raised to the power of 365 ÷ 31, that is an APY earned of 4.01%. The second calculator near the top of this page does this sum with your own statement figures.

Because it is built from real numbers, it can differ from the APY in the advertisement. The advertised APY assumes a set amount sits untouched for a year at one rate. Your statement reflects what happened: money going in and out, a rate change part way through, or a balance that moved between rate tiers.

What the result leaves out

  • Rate changes. The dollar figures hold the APY steady. On a variable-rate account the bank can change the rate after you open it.
  • Fees and minimum balances. A monthly fee, or a balance below the minimum for the advertised APY, lowers what you earn.
  • Deposits and withdrawals. The balance is treated as one amount left alone.
  • Tax. Interest is taxable income and none is deducted here.
  • Bank day counts. A bank may use a 365-day or 366-day year and its own rounding, so its APY can differ from yours in the last decimal place.

Common mistakes

  • Compounding an APY again. If you take an APY and apply daily compounding to it, you count the compounding twice. Convert it to the interest rate first.
  • Comparing one account's APY with another's interest rate. Put both on the same basis before you compare.
  • Dividing the APY by 12 for a month of interest. That overstates it slightly. One month is (1 + APY)^(1/12) − 1.
  • Reading APR on a loan as if it were APY. They are different measures for different products.
  • Ignoring the conditions. An APY that needs a minimum balance, or that lasts for a limited time, will not pay the headline figure if you do not meet the terms.

Questions people ask

How do I calculate APY from an interest rate?

Divide the rate by the number of compounding periods in a year, add 1, raise the result to the number of periods, and subtract 1. A 4% rate compounded daily is an APY of 4.08%.

How do I convert APY back to an interest rate?

Add 1 to the APY, take the root for the number of compounding periods, subtract 1, and multiply by the number of periods. An APY of 4.00% with daily compounding comes from an interest rate of about 3.92%.

Is APY the same as the interest rate?

Only when interest is compounded once a year. With more frequent compounding the APY is higher than the interest rate, because interest is earned on interest during the year.

What is the difference between APY and APR?

APY is the term for what a deposit account earns in a year, with compounding included. APR is the term you see on borrowing such as credit cards, where it is the interest rate stated as a yearly rate.

How much is 4% APY on $10,000?

It is $400.00 in one year, because APY is the percentage a balance grows by in a year. Over six months it is about $198.04. 4% is an example, not a current rate.

How much interest is one month at a given APY?

Not the APY divided by 12. One month is the balance times ((1 + APY)^(1/12) − 1). At a 4% APY, $10,000 earns about $32.74 in a month, a little under the $33.33 that dividing by 12 gives.

Do banks have to tell me the APY?

Yes. Under the Truth in Savings Act and Regulation DD, banks must disclose the annual percentage yield and the interest rate for deposit accounts, using those terms. An advertisement that states a rate of return must state it as an annual percentage yield.

Why is the APY earned on my statement different from the advertised APY?

The APY earned on a statement is worked out from the interest you were actually paid and your average daily balance in that period. Deposits, withdrawals, rate changes and tiered rates can all move it away from the advertised figure.

Sources

Figures last checked against these sources on October 10, 2026. This page gives general information and estimates, not tax, legal or financial advice.