Two savings accounts can advertise the same interest rate and still pay you different amounts. The difference is compounding — how often the interest you have already earned starts earning interest of its own. That is why banks quote APY alongside APR, and why comparing accounts by APR alone can mislead you.
This APY calculator converts an APR and a compounding frequency into the annual percentage yield, the real rate of return over a full year. Add an optional principal and it also shows the interest earned and the ending balance after one year. See more tools in our finance calculators hub.
APY Calculator
Enter the APR and how often interest is compounded to find the annual percentage yield (APY). Add a principal amount to see how much interest you would earn in one year.
Your APY result
What Is an APY Calculator?
An APY calculator takes a nominal interest rate, called the APR, and works out the annual percentage yield, or APY. The APR is the stated rate before compounding. The APY is the effective rate after compounding is taken into account, and it is always the better number to use when you compare deposit accounts.
Because interest is added to your balance during the year, you earn interest on that interest too. The more often interest is compounded, the slightly higher the APY becomes, even when the APR stays the same.
APY matters most for savings accounts, money market accounts, and certificates of deposit. To see how a balance builds over many years, try our compound interest calculator.
How Does an APY Calculator Work?
The calculator uses the standard APY formula:
APY = (1 + r ÷ n)n − 1
APY is the annual percentage yield, shown as a percentage. r is the nominal annual rate (the APR) as a decimal, so 5% becomes 0.05. n is the number of compounding periods in a year — 1 for annually, 2 for semiannually, 4 for quarterly, 12 for monthly, 52 for weekly, and 365 for daily. Dividing r by n gives the rate per period, and raising to the power n applies it across the whole year.
For continuous compounding, where interest is added constantly, the formula is different:
APY = er − 1
Here e is Euler’s number, about 2.71828. Continuous compounding gives the highest possible APY for a given APR, although the difference from daily compounding is usually small. When a principal is entered, interest earned is principal × APY, and the ending balance is principal plus that interest.
How to Use the APY Calculator
- Enter the APR as a percentage, for example 5 for 5%. Do not type the % sign.
- Choose how often interest is compounded: annually, semiannually, quarterly, monthly, weekly, daily, or continuously.
- Optionally, enter a principal amount in dollars to see the interest earned in one year and the ending balance.
- Click Calculate and read your APY, plus the interest and balance if you entered a principal.
- Try a different compounding frequency with the same APR to see how much compounding alone changes the yield.
- Click Reset to return to the default values and start a new calculation.
Our investment calculator can also model growth from regular contributions as well as interest.
Worked Example
Suppose an account pays an APR of 5% with monthly compounding, so r = 0.05 and n = 12.
APY = (1 + 0.05 ÷ 12)12 − 1 = (1.0041667)12 − 1 ≈ 0.051162, which is an APY of 5.1162%.
Now add a principal of $10,000. The interest earned in one year is $10,000 × 0.051162 ≈ $511.62, and the ending balance is $10,000 + $511.62 ≈ $10,511.62.
The APY, 5.1162%, is higher than the 5% APR. That extra is entirely the effect of monthly compounding — interest earning interest within the same year.
APY for Common Rates and Compounding Frequencies
The table shows the APY for APRs of 3%, 4%, and 5% at four compounding frequencies, calculated with the formula above.
| APR | Annual (n = 1) | Quarterly (n = 4) | Monthly (n = 12) | Daily (n = 365) |
|---|---|---|---|---|
| 3% | 3.0000% | 3.0339% | 3.0416% | 3.0453% |
| 4% | 4.0000% | 4.0604% | 4.0742% | 4.0808% |
| 5% | 5.0000% | 5.0945% | 5.1162% | 5.1267% |
Two patterns stand out. Annual compounding gives an APY equal to the APR, because there is no within-year compounding. More frequent compounding always raises the APY, but by smaller amounts — the jump from annual to quarterly is larger than from monthly to daily.
Important Points & Assumptions
This calculator assumes the APR stays fixed for the full year and that all interest is left in the account to compound. It does not include fees, taxes, penalties for early withdrawal, or minimum-balance rules, all of which can reduce what you actually earn.
It also assumes a full 365-day year and regular compounding at the frequency you select. Real accounts may credit interest on slightly different schedules, so a bank’s own figure may differ by a tiny amount. Promotional or tiered rates are not modelled here.
For long-term planning, our retirement calculator shows how savings and returns combine over many years.
Common Mistakes
The most common mistake is comparing accounts by APR instead of APY. Two accounts with the same APR but different compounding frequencies pay different amounts, and APY is the figure designed to make that comparison fair.
Another mistake is entering the rate in the wrong form — for example typing 0.05 when the field expects 5. This calculator expects the APR as a percentage number, so enter 5 for 5%.
People also expect frequent compounding to make a dramatic difference. It helps, but the effect is modest: at 5% APR, daily compounding adds only about 0.01 percentage points over monthly. A higher APR usually matters more.
How to Interpret Your Results
Read the APY as the true one-year return on money left untouched in the account. If you deposit $10,000 at a 5.1162% APY, you should expect roughly $511.62 of interest after one year, before any fees or taxes.
When comparing accounts, compare APYs first, then check fees, minimum balances, withdrawal rules, and whether the rate is fixed or variable. A slightly lower APY with no fees can beat a higher APY with charges.
Small APY differences matter more on larger balances and over longer periods. On a small, short-term balance, convenience and fees may matter more.
Frequently Asked Questions
What is the difference between APR and APY?
APR is the nominal annual rate before compounding. APY is the effective annual yield after compounding is included. For savings, APY is the better comparison figure; for borrowing, APR describes the cost of a loan.
Why is APY higher than APR?
Because interest added during the year itself earns interest. The only case where APY equals APR is annual compounding, where interest is added just once, at the end of the year.
How often is interest usually compounded?
Daily and monthly compounding are the most common for savings accounts. Certificates of deposit may compound daily, monthly, quarterly, or annually, depending on the bank and the term.
Does more frequent compounding always mean more interest?
Yes, for the same APR and principal, more frequent compounding always gives a slightly higher APY. The increases get smaller as compounding gets more frequent, and continuous compounding is the upper limit.
What is a good APY?
There is no single good APY, because rates move with the wider economy and differ by account type. Compare the APY with other accounts available to you at the time, and weigh fees and access rules alongside the rate.
Can APY change after I open an account?
Yes, if the account has a variable rate, the bank can change the rate and therefore the APY. Fixed-rate certificates of deposit normally keep the same APY for their full term.
References
For how APY must be disclosed to consumers in the United States, see the Federal Deposit Insurance Corporation (FDIC), which covers APY disclosure under Regulation DD, the Truth in Savings rules.
Disclaimer: This calculator and article provide general educational information only and are not financial advice. Rates, rules, and account terms change and vary by institution, so check the current terms with your bank or credit union and consider speaking to a qualified financial adviser before making decisions about your money.