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APY Calculator

Annual percentage yield from a nominal rate and compounding frequency, plus the interest and ending balance for your deposit and term. 5% monthly is 5.116%. How it works

Use the APY Calculator

Annual Percentage Yield (APY)
5.116%

Your deposit

On a $10,000.00 deposit, you would earn$511.62in interest after 1 year.

Balance at the end of the term:$10,511.62

APY includes the effect of compounding, so it is usually higher than the nominal rate. It is not adjusted for inflation. The balance assumes the rate stays the same for the whole term and that nothing is added or taken out. The more often interest compounds, the higher the APY for the same nominal rate.

About the APY Calculator

5% compounded monthly has an APY of 5.116%, so $10,000 earns $511.62 in a year. APY = (1 + r ÷ n)^n − 1, where r is the nominal rate and n is the number of times a year interest compounds. The APY calculator takes a nominal rate and a compounding frequency: yearly, twice a year, quarterly, monthly, weekly or daily.

APY by nominal rate and compounding frequency

Nominal rateAnnuallyQuarterlyMonthlyDaily
1%1.000%1.004%1.005%1.005%
2%2.000%2.015%2.018%2.020%
3%3.000%3.034%3.042%3.045%
4%4.000%4.060%4.074%4.081%
5%5.000%5.095%5.116%5.127%
6%6.000%6.136%6.168%6.183%

The big figure the calculator shows, to three decimals. Daily compounding uses 365 periods a year and weekly uses 52.

Frequently asked questions

What is the difference between APY and the interest rate?
The nominal interest rate leaves compounding out and the APY includes it. A 5% rate compounded monthly pays 5.116% over a year, so the APY is the higher number whenever interest compounds more than once a year.
How do I calculate APY from the interest rate?
Divide the rate by the number of compounding periods n, add 1, raise the result to the power n and subtract 1. For 4.5% compounded daily, (1 + 0.045 ÷ 365)^365 − 1 = 4.602%.
Does compounding more often make a big difference?
Not much. At 5% the APY is 5.000% with yearly compounding and 5.127% with daily compounding, a gap of 0.127 percentage points. On $10,000 that is $500.00 against $512.67 in a year.
What nominal rate gives a 5% APY?
With monthly compounding the nominal rate is n × ((1 + APY)^(1 ÷ n) − 1) = 12 × (1.05^(1 ÷ 12) − 1), about 4.889%. Entering 4.889 with monthly compounding returns an APY of 5.000%.
Is my bank’s APY the same as this result?
It can differ slightly. Under Regulation DD a bank works out APY from the interest actually earned over the actual number of days in the term, on a 365-day year. This calculator applies the compounding formula to the nominal rate you enter.
Is APY adjusted for inflation?
No. APY is a yearly rate before inflation, taxes and fees, so it is not a real rate of return.

Comparing accounts that compound at different frequencies

Savers compare a savings account, money market account or CD that quotes a nominal rate with one that quotes an APY, and see how much the compounding frequency matters. APY is the yearly rate with compounding included, so accounts that compound at different frequencies can be compared on one figure. It is not adjusted for inflation. A 4.5% rate compounded daily, for example, is an APY of 4.602%. Banks work out their quoted APY from the interest actually earned over the actual days in the term, so it can differ slightly from this formula.

Compounding formula

APY = (1 + r ÷ n)^n − 1, where r is the nominal rate as a decimal and n is the number of compounding periods a year (1, 2, 4, 12, 52 or 365). Example: 5% compounded monthly is (1 + 0.05 ÷ 12)^12 − 1 = 5.116%, and $10,000 grows to $10,511.62 in a year, which is $511.62 of interest. At 5% with annual compounding the APY equals the rate, 5.000%, and daily compounding gives 5.127%. To go the other way, the nominal rate for a given APY is n × ((1 + APY)^(1 ÷ n) − 1): a 5% APY compounded monthly needs a nominal rate of about 4.889%. More frequent compounding always gives a slightly higher APY for the same nominal rate. At 5% the APY is 5.000% yearly, 5.062% twice a year, 5.095% quarterly, 5.116% monthly, 5.125% weekly and 5.127% daily. Type a deposit and a term in years or months for the interest and the ending balance: deposit × (1 + r ÷ n)^(n × years). $25,000 at 5% compounded monthly for 5 years ends at $32,083.97, $7,083.97 of interest, and $10,000 for 6 months earns $252.62. The rate may be from −100% to 1,000% and the term up to 100 years.

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