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Free APY Calculator

Turn a nominal annual rate (APR) and its compounding frequency into the effective annual percentage yield (APY), and see the interest a balance earns in one year.

Annual Percentage Yield (APY)
5.1162%
Interest earned (1 year)
$511.62
Balance after 1 year
$10,511.62

APY = (1 + (r/100) ÷ n)n − 1. It is the effective yearly return after compounding, ignoring fees and taxes.

Same rate at different compounding frequencies

CompoundingPeriods / yrAPYInterest (1 yr)
Annually15.0000%$500.00
Semi-annually25.0625%$506.25
Quarterly45.0945%$509.45
Monthly125.1162%$511.62
Daily3655.1267%$512.67

More frequent compounding raises APY slightly; the gain shrinks as you approach continuous compounding.

Estimate only. This calculator provides estimates based on the values you enter and the formula shown. It is not financial advice and may not reflect every fee, tax, or lender requirement. Check figures with a qualified professional before making financial decisions.

Quick answer

APY (annual percentage yield) is the effective yearly return after compounding. With nominal rate r% compounded n times per year, APY = (1 + (r/100)/n)^n − 1. For example, a 5% rate compounded monthly gives (1 + 0.05/12)^12 − 1 = 5.1162%. More frequent compounding raises APY, while annual compounding makes APY equal to the nominal rate.

Formula & method

Enter the nominal annual rate (often shown as APR), choose how many times per year interest compounds (n), and optionally a principal. The calculator converts the rate to a decimal, divides it by n to get the periodic rate, applies (1 + periodic rate) raised to the power n, and subtracts 1 to express the effective annual percentage yield. If you supply a principal P, the one-year interest is P × APY and the ending balance is P × (1 + APY). A comparison table shows the same nominal rate under annual, semi-annual, quarterly, monthly, and daily compounding so you can see how frequency changes the yield. Results exclude fees, taxes, and any rate changes during the year.

Examples

Example 1: 5% compounded monthly
Input
Rate = 5%, n = 12 (monthly), Principal = $10,000
Result
APY = 5.1162%; interest = $511.62; balance = $10,511.62
Why
APY = (1 + 0.05/12)^12 − 1 = 1.0041667^12 − 1 = 0.051162, i.e. 5.1162%. On $10,000 that is 10,000 × 0.051162 = $511.62 of interest, ending at $10,511.62.
Example 2: 4.5% compounded daily
Input
Rate = 4.5%, n = 365 (daily), Principal = $5,000
Result
APY = 4.6025%; interest = $230.12
Why
APY = (1 + 0.045/365)^365 − 1 = 0.046025, i.e. 4.6025%. Daily compounding earns slightly more than the 4.5% nominal rate. On $5,000: 5,000 × 0.046025 = $230.12.
Example 3: 6% compounded quarterly
Input
Rate = 6%, n = 4 (quarterly), Principal = $2,000
Result
APY = 6.1364%; interest = $122.73
Why
APY = (1 + 0.06/4)^4 − 1 = 1.015^4 − 1 = 0.061364, i.e. 6.1364%. On $2,000: 2,000 × 0.061364 = $122.73 of interest in one year.
Example 4: 5% compounded annually
Input
Rate = 5%, n = 1 (annually)
Result
APY = 5.0000%
Why
With annual compounding APY = (1 + 0.05/1)^1 − 1 = 0.05 = 5.0000%. When n = 1, APY equals the nominal rate exactly because interest is added only once per year.

When to use this tool

  • Comparing savings accounts, CDs, or money market accounts that quote different nominal rates and compounding frequencies on an apples-to-apples basis.
  • Converting a bank's stated APR into the true effective yield (APY) you will actually earn over a year.
  • Estimating one year of interest on a known balance before fees and taxes.
  • Checking how much extra a 'daily compounding' account really pays versus monthly or quarterly at the same nominal rate.

Common mistakes

  • Confusing APR with APY. APR is the nominal stated rate; APY is the effective rate after compounding. APY is always greater than or equal to APR, and they are equal only when interest compounds once per year.
  • Dividing the rate by n twice. The periodic rate is (r/100)/n applied once; you do not divide again before raising to the power n.
  • Using the wrong n. Monthly is 12, quarterly is 4, daily is 365, and annual is 1 — not the number of years you plan to invest. The exponent n is compounding periods per year.
  • Assuming higher frequency means dramatically higher returns. Going from monthly to daily adds only a tiny amount; the limit (continuous compounding) is e^(r) − 1, a hard ceiling.
  • Comparing accounts by APR instead of APY. Two accounts with the same APR but different compounding frequencies pay different real returns, so always compare APY.

Frequently asked questions

What is the difference between APR and APY?

APR (annual percentage rate) is the nominal stated rate without compounding. APY (annual percentage yield) is the effective rate after compounding is applied. For a deposit, APY = (1 + (APR/100)/n)^n − 1. APY is always at least as large as APR and they are equal only when interest compounds once per year (n = 1).

How is APY calculated?

APY = (1 + (r/100)/n)^n − 1, where r is the nominal annual rate as a percentage and n is the number of compounding periods per year. Multiply the result by 100 to show it as a percentage. For r = 5 and n = 12, APY = (1 + 0.05/12)^12 − 1 = 5.1162%.

Does more frequent compounding always give a higher APY?

Yes, but with diminishing returns. For a fixed nominal rate, increasing n raises APY slightly each time, approaching a ceiling of e^(r/100) − 1 (continuous compounding). For a 5% rate that ceiling is about 5.1271%, so monthly (5.1162%) is already very close to daily (5.1267%).

Is APY the same as the interest rate?

Only when interest compounds once a year. The 'interest rate' usually means the nominal rate (APR). Because of compounding, the APY you actually earn is a bit higher whenever interest is added more than once per year.

How much interest will I earn in a year?

Interest for one year is principal × APY. If you deposit $10,000 at an APY of 5.1162%, you earn 10,000 × 0.051162 = $511.62, ending the year with $10,511.62. This estimate ignores fees, taxes, deposits, and withdrawals.

Does this calculator account for taxes or fees?

No. It shows the gross APY and gross interest based purely on the rate and compounding frequency. Account fees, withdrawal penalties, and income taxes reduce your real, after-tax return, so treat the figures as a before-cost estimate.

What compounding frequency should I choose?

Use the frequency your account actually uses: monthly (12), quarterly (4), daily (365), or annually (1). Banks disclose this in the account terms. If you only have the APY and want to compare, the frequency matters less because APY already reflects compounding.

Sources & references

External references open in a new tab. We are independent and not affiliated with these organizations.

Disclaimer

This calculator provides estimates based on the values you enter and the formula shown. It is not financial advice and may not reflect every fee, tax, or lender requirement. Check figures with a qualified professional before making financial decisions.

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