APY Calculator
APY Calculator
The nominal annual interest rate before compounding effects
Starting balance or lump sum deposit
Additional deposits made at each deposit frequency interval
Enter Your Rate to Get Started
Enter an interest rate and compounding frequency above to see APY, projected growth, and compounding comparisons.
Important
This calculator is provided for general information only and is not financial, tax, or legal advice. Results are estimates and do not reflect your full circumstances, current rates, fees, or eligibility rules. Speak to a qualified professional before making a financial decision.
Convert APR to APY, reverse-calculate, and project savings growth
The Annual Percentage Yield (APY) is one of the most important numbers in personal finance — yet it's often misunderstood or confused with the Annual Percentage Rate (APR). Understanding the difference between these two rates can mean thousands of dollars in your savings account over time. Our free APY Calculator helps you convert between APR and APY instantly, project how your savings will grow through compound interest, and compare different compounding frequencies side by side. APY measures the actual rate of return on an investment or savings account over one year, taking into account the effect of compounding interest. Unlike APR, which simply states the nominal interest rate, APY reflects how interest compounds — whether daily, monthly, quarterly, or continuously. The more frequently interest compounds, the higher the effective annual yield will be compared to the stated nominal rate. For savers, APY is the number that matters most. When your bank advertises a high-yield savings account or certificate of deposit (CD), they're quoting APY because it shows you exactly how much your money will grow in one year. A savings account with a 5% APR compounded daily will have an APY of approximately 5.127%, which means your $10,000 deposit will earn $512.70 in a year — not just $500. This calculator supports three powerful modes: APR to APY conversion (the most common use case), APY to APR reverse calculation (useful when you know the yield and want the nominal rate), and a full Growth Estimate mode that projects your final balance, total interest earned, and year-by-year savings schedule. You can also add recurring deposits — weekly, monthly, or any frequency — to simulate real-world savings contributions. Beyond basic conversion, this tool shows you the compounding frequency comparison table, which displays what APY you'd achieve at every compounding interval from daily to annually using the same nominal rate. This makes it easy to understand why daily compounding accounts offer a slightly higher yield than monthly compounding accounts at the same APR. We also calculate 'years to double' using both the exact formula and the classic Rule of 72 approximation. If your APY is 6%, the Rule of 72 tells you your money will double in approximately 12 years. The exact formula confirms this more precisely. This is a powerful way to set long-term savings goals and understand the true power of compound interest. Whether you're comparing high-yield savings accounts, evaluating CD rates, analyzing money market accounts, or planning long-term investment growth, this APY Calculator gives you the complete picture with visual charts, a downloadable yearly growth schedule, and the ability to copy or print your results.
Understanding APY and Compound Interest
What Is APY?
Annual Percentage Yield (APY) is the effective annual rate of return on an investment, savings account, or deposit product after accounting for compounding interest. It is always expressed as a percentage and represents the total amount of interest you earn over one full year. APY differs from APR (Annual Percentage Rate) in that APR is a simple nominal rate that does not account for compounding, while APY reflects the actual yield including the compounding effect. The formula for APY is: APY = (1 + r/n)^n - 1, where r is the nominal annual interest rate and n is the number of compounding periods per year. For continuous compounding, the formula becomes APY = e^r - 1. Banks and financial institutions are required by law (the Truth in Savings Act in the US) to disclose APY on deposit products, making it the standard benchmark for comparing savings accounts, CDs, and money market accounts.
How Is APY Calculated?
APY is calculated by taking the nominal annual interest rate (APR) and applying the compounding formula. For periodic compounding: APY = (1 + r/n)^n - 1, where r is the APR expressed as a decimal and n is the number of compounding periods per year. For example, a 5% APR compounded monthly gives APY = (1 + 0.05/12)^12 - 1 = 0.05116, or approximately 5.116%. The reverse calculation — finding APR from APY — uses: APR = n × ((1 + APY)^(1/n) - 1). For continuous compounding, APY = e^r - 1, and the reverse is APR = ln(1 + APY). When calculating future value with recurring deposits, the formula uses iterative period simulation: at each compounding period, the balance grows by the per-period rate, then deposits are added according to the deposit schedule. This approach accurately models real savings accounts where you make periodic contributions.
Why Does APY Matter?
APY matters because it is the only apples-to-apples comparison number when evaluating deposit accounts. Two banks might both advertise '5% interest,' but if one compounds daily and the other compounds annually, the daily compounding account will pay you more money. APY accounts for this difference automatically. For a $100,000 deposit at 5% APR: annually compounded gives APY = 5.000% and $5,000 in interest; monthly compounding gives APY = 5.116% and $5,116; daily compounding gives APY = 5.127% and $5,127. Over many years and larger balances, these differences become substantial. Understanding APY also helps you evaluate the power of compound interest over long time horizons — a concept that Albert Einstein reportedly called 'the eighth wonder of the world.' Higher APY means your interest earns interest, creating exponential growth rather than linear growth.
Limitations and Considerations
While APY is an excellent tool for comparing deposit products, it has important limitations. First, APY assumes the rate stays constant for the entire year — variable-rate accounts (like many high-yield savings accounts) can change their rates frequently, so the advertised APY may not reflect what you actually earn over a full year. Second, APY does not account for fees: a savings account with a 5% APY but a $5/month maintenance fee may actually be less profitable than a 4% APY account with no fees. Third, APY only applies to one year — for multi-year projections, you need to use compound interest formulas with the APY rate. Fourth, taxes on interest income will reduce your effective yield. Finally, APY comparisons are only meaningful for accounts with the same compounding frequency basis; always compare using the actual APY figure, not the nominal APR. This calculator provides projections for educational purposes; actual account performance may vary.
How to Use the APY Calculator
Choose Your Calculation Mode
Select from three modes at the top: 'APR to APY' to find the effective yield from a nominal rate, 'APY to APR' to reverse-engineer the nominal rate from a known yield, or 'Growth Estimate' for a full projection with year-by-year breakdown.
Enter Your Rate and Compounding Frequency
Enter the interest rate and select how often your account compounds — daily, monthly, quarterly, semi-annually, annually, or continuously. Most savings accounts and CDs compound daily or monthly. The compounding frequency significantly affects your effective yield.
Add Principal, Term, and Optional Deposits
In Growth Estimate or APR-to-APY mode, enter your initial deposit amount and the number of years. Optionally add a recurring deposit amount and frequency to model ongoing contributions — ideal for simulating a high-yield savings account with automatic transfers.
Review Results and Export
Your APY, final balance, total interest, and compounding comparison appear instantly. Use the 'Years to Double' section to see long-term projections, the comparison chart to evaluate different compounding frequencies, and Export CSV to download a year-by-year growth schedule.
Frequently Asked Questions
What is the difference between APR and APY?
APR (Annual Percentage Rate) is the nominal interest rate without accounting for compounding — it simply states the base interest charge or yield for the year. APY (Annual Percentage Yield) is the effective annual rate that includes the effect of compounding, showing the true return you earn over a full year. For savings accounts, APY is always equal to or higher than APR because compounding adds interest on top of previously earned interest. For example, a 6% APR compounded monthly yields an APY of approximately 6.168%. Banks are required by US law (Truth in Savings Act) to disclose APY on deposit products so consumers can make fair comparisons.
Which compounding frequency gives the highest APY?
For the same nominal APR, more frequent compounding always produces a higher APY. The ranking from lowest to highest APY is: annually → semi-annually → quarterly → bi-monthly → monthly → semi-monthly → bi-weekly → weekly → daily → continuous. However, the differences are relatively small in practice. At a 5% APR: annual compounding gives APY = 5.000%, monthly gives 5.116%, daily gives 5.127%, and continuous gives 5.127%. The gap between daily and continuous compounding is less than 0.001%, so daily compounding is essentially equivalent to continuous for most practical purposes.
What is continuous compounding and when is it used?
Continuous compounding is a theoretical concept where interest is calculated and added to the balance at every possible instant — an infinite number of times per year. The formula for continuous APY is APY = e^r - 1, where e ≈ 2.71828 (Euler's number) and r is the nominal annual rate. In practice, true continuous compounding is used in certain financial models, physics of exponential growth, and some derivative pricing models, but no bank or savings account actually compounds continuously. It serves as the mathematical upper limit for a given APR: no matter how frequently a bank compounds, the APY can never exceed the continuous compounding APY.
What is the Rule of 72 and how accurate is it?
The Rule of 72 is a simple mental math shortcut to estimate how long it takes to double your money at a given annual return: divide 72 by the APY percentage. At 6% APY, 72 ÷ 6 = 12 years to double. The exact formula is: years = ln(2) / ln(1 + APY). The Rule of 72 is most accurate for rates between 2% and 12%; at higher rates, it slightly underestimates the doubling time. At 6%, the rule gives 12.00 years and the exact formula gives 11.90 years — a difference of only about 1 month. The rule is a quick and surprisingly accurate approximation for everyday savings planning and investment thinking.
How does adding regular deposits change my APY calculation?
Regular deposits do not change your APY — that is purely a function of the nominal rate and compounding frequency. However, they dramatically change your final balance and total interest earned. With regular deposits, each new deposit starts earning compound interest immediately (or at the next compounding date), creating a snowball effect. This calculator simulates the exact growth by applying the per-period growth rate at each compounding interval and adding deposits according to your chosen deposit frequency. The result is a year-by-year schedule showing exactly how your balance grows, split between your contributions and the interest earned on all contributions over time.
How do I convert APY back to APR?
To find the APR (nominal rate) from a known APY, use the reverse formula: APR = n × ((1 + APY)^(1/n) - 1), where n is the number of compounding periods per year. For continuous compounding, APR = ln(1 + APY). This is useful when a bank advertises an APY and you want to know the underlying nominal rate for calculations or comparisons. Switch this calculator to 'APY to APR' mode, enter the APY and compounding frequency, and the tool will show you the exact nominal rate. For example, a 5.127% APY with daily compounding corresponds to an APR of approximately 5.000%.