What is Annual Percentage Yield (APY) in simple words?

APY (Annual Percentage Yield) is the amount your money will grow by over a year because of interest, including interest on the interest already earned. It's the fairest way to compare savings and certificates of deposit accounts because it expresses the effects of compound interest as a percentage.

What's the difference between APY and APR?

APY is an interest rate that takes into account compound interest and is used for savings accounts. APR (Annual Percentage Rate) is usually a stated interest rate that does not necessarily include compound interest, and is used for loans and credit cards. For the same account, APY will always be higher than APR.

Is the APY daily, monthly or annual compounding?

The APY already takes into account the type of interest compounding used by the particular account. If the stated rate is the same, more frequent compounding (e.g., daily) will result in a slightly higher APY than annual compounding.

What is 5% APY on $1,000?

At an annual percentage yield (APY) of 5%, the interest on a $1,000 principal would be about $50 per year, so that the account balance is $1,050. Because the APY is already an annual value, the annual interest earned is simply the account balance multiplied by the APY.

How do you calculate nominal interest rate from APY?

Leave the field for nominal interest rate blank and enter the APY. Select how often compounding occurs. This calculator reverses the formula for APY to give back the stated interest rate that produces this effective interest rate.

APY Calculator

Rate and compounding

Nominal interest rate (APR)

Compounding frequency

Dropdown list for Compounding Frequency

APY (annual percentage yield)

Your savings

Initial deposit

Savings period (years)

Add a monthly contribution

Model a fixed deposit you add every month, on top of the starting amount.

Ending balance

Annual percentage yield (APY)

Ending balance: $
Interest earned: $
Total deposited: $

Boost from compounding: %

Compounding lifts your 5% nominal rate to an APY of 5.12%.

Charts and schedule

Show the balance breakdown

Split the ending balance into your deposits and the interest earned.

Show the growth chart

Plot the balance year by year.

Show the year-by-year table

A full table of each year's start, deposits, interest, and end balance.

Where your ending balance comes from ($)

Year-by-year savings schedule
Year	Start ($)	Interest ($)	End ($)
1	1,000	51.16	1,051.16
2	1,051.16	53.78	1,104.94
3	1,104.94	56.53	1,161.47
4	1,161.47	59.42	1,220.9
5	1,220.9	62.46	1,283.36

The Annual Percentage Yield (APY) is the actual annual return earned on savings accounts, certificates of deposit and other interest-bearing accounts that takes compound interest into account. The simple interest rate alone does not give a complete picture because it doesn't indicate how often the interest is credited to the balance. This calculator allows you to convert an advertised interest rate into APY, convert APY into an advertised interest rate or predict how much money will grow over time.

What is an APY?

The APY indicates the percentage that your balance will increase by annually, including interest earned on the interest itself. That last part is called compounding interest. When a bank credits an account with monthly or daily interest, those newly accrued interest amounts also begin to earn interest, so at the end of the year you'll have more than what would be expected based on the advertised rate alone.

Because the APY takes into account interest on interest, it is a more accurate figure when comparing accounts. Even if different accounts offer the same interest rate, the one with more frequent compounding will have a higher APY.

How is APY calculated?

The APY depends on the nominal interest rate and number of compounding periods per year that apply to an account.

APY = \left(1 + \frac{r}{n}\right)^{n} - 1

In this formula, r is the nominal annual interest rate expressed as a decimal and n is the number of compounding periods per year. For example, if you have a savings account that pays monthly interest at an annual rate of 5 percent, then r would be .05 and n would be 12.

APY = \left(1 + \frac{0.05}{12}\right)^{12} - 1 \approx 0.05116 = 5.116\%

A return of 5.116 percent is slightly above the stated interest rate of 5 percent. This difference is the value created by compounding. Conversely, if the nominal interest rate is left blank and instead the effective annual yield (APY) is entered, this calculator can reverse the formula to determine the stated interest rate that would produce that APY.

The Difference Between APY and APR

APY and APR represent interest rates from different perspectives. The APY is the return that shows savers how much they can earn in a year on an account, taking into account compound interest. The APR is the stated rate of interest, mainly used for loans and credit cards, and usually does not take compounding into account. When saving, one should look for a higher APY, while with borrowing, a lower APR will reduce costs. On the same account, the APY will always be higher than the nominal APR, and they are only equal when interest is compounded annually.

How APY Changes With Compounding Frequency

If the nominal interest rate is set at 5 percent and only the frequency of compounding changes, then the more frequent the compounding occurs, the higher will be the APY.

Compounding	Periods per year	APY on a 5% rate
Annual	1	5.00%
Semi-annual	2	5.06%
Quarterly	4	5.09%
Monthly	12	5.12%
Daily	365	5.13%

The rate of growth is gradually decreasing. The increase when switching from annual compounding to monthly compounding is larger than the increase when switching from monthly to daily compounding. Once a certain value is exceeded, the return changes little even if the frequency of compounding is increased.

Forecast of savings growth:

If you know the APY, then this tool can help you project your balance into the future. Enter the initial deposit amount and number of years, and the tool will calculate the return on an annual basis. If you add in regular monthly deposits, it will calculate the growth rate based on how long each deposit is invested for. If you put $1,000 in a savings account with 5 percent APY and leave it there for five years without making additional deposits, your balance would be:

1{,}000 \times (1 + 0.05)^{5} \approx 1{,}276.28

This means that apart from the capital invested, interest of 276.28 will accrue. Detailed charts and annual tables show the ending balance amount, broken down into the amount of capital invested and the resulting interest.

This tool is for educational and planning purposes only and does not constitute financial advice. The interest rates published are subject to change, and banks may charge interest with different rounding rules so the actual return could vary slightly. Please check account terms before basing any decisions on specific figures.

Frequently asked questions

What is Annual Percentage Yield (APY) in simple words?: APY (Annual Percentage Yield) is the amount your money will grow by over a year because of interest, including interest on the interest already earned. It's the fairest way to compare savings and certificates of deposit accounts because it expresses the effects of compound interest as a percentage.
What's the difference between APY and APR?: APY is an interest rate that takes into account compound interest and is used for savings accounts. APR (Annual Percentage Rate) is usually a stated interest rate that does not necessarily include compound interest, and is used for loans and credit cards. For the same account, APY will always be higher than APR.
Is the APY daily, monthly or annual compounding?: The APY already takes into account the type of interest compounding used by the particular account. If the stated rate is the same, more frequent compounding (e.g., daily) will result in a slightly higher APY than annual compounding.
What is 5% APY on $1,000?: At an annual percentage yield (APY) of 5%, the interest on a $1,000 principal would be about $50 per year, so that the account balance is $1,050. Because the APY is already an annual value, the annual interest earned is simply the account balance multiplied by the APY.
How do you calculate nominal interest rate from APY?: Leave the field for nominal interest rate blank and enter the APY. Select how often compounding occurs. This calculator reverses the formula for APY to give back the stated interest rate that produces this effective interest rate.

Related calculators

Effective Annual Interest Rate CalculatorConvert a nominal interest rate into the effective annual rate (EAR / APY) for any compounding frequency, including continuous compounding, and solve the nominal rate in reverse.

Annual Interest Rate CalculatorFind the annual interest rate on a loan or investment from the principal, final amount, and time. Solve for any variable under simple, compound, or continuous interest, and see the effective rate (APY).

Savings CalculatorProject how a savings account grows with an initial deposit, regular contributions, and compound interest. Adjust for tax and inflation, and solve for the deposit, rate, time, or savings goal.

CD Rate CalculatorWork out what a certificate of deposit pays at maturity, then check the tax, the early withdrawal penalty, a rival bank's APY, and whether the yield beats inflation.

CD CalculatorWork out what a certificate of deposit is worth at maturity from either an APY or an interest rate plus compounding. Price the early-withdrawal penalty, compare against another bank's rate, and see the balance after tax and inflation.

Compound Interest CalculatorCalculate compound interest and the future value of a deposit, with optional regular contributions, any compounding frequency, the effective annual rate (APY), a simple-versus-compound comparison, a growth chart, and a year-by-year table. Works in reverse to solve for the rate, time, or starting amount.

Disclaimer: This calculator is provided for general informational and educational purposes only. Our calculators are under active development, and results may be inaccurate, incomplete, or unsuitable for your situation. Always verify the figures independently and seek advice from a qualified professional before relying on them. We make no warranties and accept no liability for any loss or decision arising from use of this tool.

References

Investopedia: Annual Percentage Yield (APY)
Definition, formula, and worked examples for APY.
Consumer Financial Protection Bureau: What is APY?
How APY works under the Truth in Savings Act.
Investor.gov: Compound Interest Calculator and Saving Basics
U.S. SEC explainer on compounding and saving.