Finance

APY Calculator

Calculate the Annual Percentage Yield (APY) from the nominal APR, or vice-versa, and see projections with compounding.

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Last updated: June 2026

Type in your APR or APY — changing one automatically calculates the other based on compounding frequency.


The initial amount you deposit into the account. Enter 0 or leave blank to just calculate the rates without investment projections.
How often interest compounds. Daily compounding creates slightly more growth than monthly compounding because you earn interest on your interest sooner!
The Annual Percentage Rate (APR) is the base advertised interest rate, not including compounding.
The Annual Percentage Yield (APY) represents the actual interest you earn over a year because it includes compounding.

Click "Calculate" to view results.

Nominal APR

Advertised Rate

Effective APY

Real Rate of Return

Compounding Profit

Compounding edge

Total Deposits
Interest Earned
Final Balance

Enter an initial deposit or regular deposit to generate a savings projection chart.

Enter an initial deposit or regular deposit to generate a year-by-year growth table.

Year Deposits Added Interest Earned Year End Balance

APY & APR Formulas

Nominal rate (APR) and Effective yield (APY) are related through the compound interval. Since compounding adds interest back to your balance, the yield is always higher than the APR.

APR to APY: APY = (1 + r/n)n - 1
APY to APR: APR = n × [(1 + APY)1/n - 1]

Where: r = nominal APR as a decimal, n = compound periods per year (e.g. 12 for monthly), and APY is expressed as a decimal.

Your Step-by-Step Calculation

1. Compound periods (n) = per year
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Reviewed by Applied Math & Finance Specialists Editorial Policy
Updated: July 2026 Fact-Checked

What Is the APY Calculator?

The APY Calculator converts a stated Annual Percentage Rate (APR) into the true Annual Percentage Yield (APY) based on your compounding frequency. While banks advertise APR, the actual return you earn depends on how often interest compounds — making APY the more accurate measure for comparing savings products.

The Truth in Savings Act (TISA) in the United States requires financial institutions to disclose APY on deposit accounts, ensuring consumers can make fair comparisons. This calculator helps you verify those disclosures and compute APY for any compounding schedule.

The APY Formula

APY = (1 + APR/n)^n - 1
where APR is the nominal annual rate (as a decimal) and n is the number of compounding periods per year. The more frequently interest compounds, the higher the APY relative to APR.

How to Use the APY Calculator

Using this calculator is straightforward. Enter your known values into the fields below, and the solver will compute the result immediately. Here is what each input represents:

Initial Deposit ($) Example input: 1000
Nominal APR (%) Example input: 5
APY (%) Example input: 5.12
Term (Years) Example input: 5
Worked Example

Worked Example: Converting a 4.5% APR Savings Account to APY

Problem: Your bank offers a savings account with a 4.5% APR, compounded daily (365 times per year). What is the actual APY you will earn?

1. Identify the Variables

APR = 4.5% = 0.045 (decimal). Compounding periods per year (n) = 365.

2. Calculate the Periodic Rate

Divide APR by the number of compounding periods: 0.045 / 365 = 0.00012329.

\frac{0.045}{365} = 0.00012329

3. Apply the APY Formula

APY = (1 + 0.00012329)^365 − 1 = 1.04603 − 1 = 0.04603.

APY = (1.00012329)^{365} - 1 = 0.04603

4. Convert to Percentage

0.04603 × 100 = 4.603%. The daily compounding adds an extra 0.103% yield over the stated 4.5% APR.

APY = 4.603\%
Final Result APY = 4.603%. On a $10,000 deposit, this means earning $460.30/year instead of $450.00 — an extra $10.30 from daily compounding.

How to Calculate APY Step-by-Step

Understanding the underlying solution workflow helps build mathematical intuition:

1
Identify and note down the given values for: Initial Deposit ($), Nominal APR (%), APY (%), Term (Years).
2
Substitute your values into the standard mathematical formula for APY Calculator.
3
Perform the required logical or mathematical steps to calculate the final output.
4
Round the final calculated answer to the required decimal accuracy or significant figures.

Real-World Applications of APY Calculator

Comparing High-Yield Savings Accounts

Online banks and credit unions advertise different APRs and compounding schedules. Converting all offers to APY lets you identify which account truly pays the highest return.

Certificate of Deposit (CD) Ladder Planning

When building a CD ladder with different maturities and rates, APY ensures you compare the actual yield of each rung, not just the advertised rate.

Understanding DeFi Yield Farming Returns

Crypto yield farming platforms often quote APR. Converting to APY reveals the true return when rewards auto-compound hourly or daily.

Common Pitfalls & Mistakes to Avoid

Comparing APR from One Account to APY from Another

Always convert both accounts to APY (or both to APR) before comparing. Mixing the two metrics will give misleading results.

Assuming Higher Compounding Frequency Always Matters

The APR-to-APY gap narrows as rates decrease. At 0.5% APR, the difference between monthly and daily compounding is negligible — focus on the rate itself.

Ignoring Introductory Rate Expirations

Some banks offer promotional APYs that revert to a lower rate after 6-12 months. Calculate the blended effective APY across the full period.

Key Terminology Glossary

APR (Annual Percentage Rate) The nominal annual interest rate stated by the bank, without factoring in the effect of compounding within the year.
APY (Annual Percentage Yield) The effective annual return that accounts for how often interest compounds. APY ≥ APR when compounding happens more than once per year.
Compounding Frequency The number of times per year that interest is calculated and added to the balance — daily (365), monthly (12), quarterly (4), or annually (1).
Effective Interest Rate Another term for APY. It reflects the actual percentage gain on your deposit over one full year, inclusive of all compounding effects.

Expert Tips for APY Calculator

  • If you're comparing savings accounts, always compare the APY rather than the APR. APY is the true reflection of what you'll earn.
  • The more frequently interest is compounded, the higher the APY will be relative to the nominal APR.
  • Bidirectional conversion: Type in APR to find APY, or type in APY to find the APR needed.
  • Consider regular deposits: Adding even a small regular deposit makes compounding grow your balance significantly faster.

About the APY Calculator

The APY Calculator is maintained by Basic Math Tools, an educational platform committed to providing accurate STEM and financial computing tools. Every tool processes calculations transparently in your browser for privacy and speed.

If you have suggestions or request additional features, please review our Editorial Policy or contact our math team.

Frequently Asked Questions

What is APY (Annual Percentage Yield)?
APY is the real rate of return on a savings account or investment, taking into account the effect of compound interest. It shows the total interest earned in a year as a percentage.
What is the difference between APR and APY?
APR (Annual Percentage Rate) is the nominal interest rate that does not account for compounding. APY accounts for compounding and represents the actual amount of interest earned or paid over a year.
How is APY calculated from APR?
The formula is APY = (1 + r/n)^n - 1, where r is the nominal APR as a decimal, and n is the number of compounding periods per year.
How is APR calculated from APY?
The formula is APR = n * [(1 + APY)^(1/n) - 1], where APY is the annual percentage yield as a decimal, and n is the compounding periods per year.
How does the APY Calculator calculate results?
The calculator applies the standard mathematical formula used in finance. Enter your known values, and it computes the result using the same methods taught in textbooks, displaying each step for verification.