The APY Calculator computes the Annual Percentage Yield from a nominal interest rate and compounding frequency. APY shows the true annual return including compounding — the key metric for comparing savings accounts, CDs, and any interest-bearing product where compounding frequency varies.
5.1162%
0.1162%
$511.62
$10,511.62
5.1162%
0.1162%
$511.62
$10,511.62
A savings account advertises 5.00% APR. Another offers 4.88% APY. Which actually earns more? The answer is APY — always — because APY already accounts for compounding while APR does not. The calculator for APY converts any nominal rate and compounding frequency into the effective annual yield, making fair comparisons between financial products with different compounding schedules instant and unambiguous.
APY incorporates the compounding frequency n (times per year) into the effective annual return:
APY = (1 + r/n)^n − 1
where r is the nominal annual interest rate (as a decimal). For a nominal rate of 5% with different compounding frequencies:
At 5% nominal, daily compounding earns USD 51.27 on USD 1,000 in a year versus USD 50.00 for annual compounding — a modest but real difference that compounds over time. Use this online calculator for any nominal rate and compounding schedule. The APR calculator covers the borrowing-side equivalent for loans.
APY and APR are related but serve different purposes in financial disclosure:
When a bank advertises 5.00% APR on a savings account and 5.12% APY, both are truthful and refer to the same product — the APY simply shows what you actually earn after compounding. The same institution's mortgage at 6.5% APR does not compound in the same way because mortgage payments reduce principal continuously.
In a competitive savings environment, the APY difference between institutions can be significant. During high-rate periods, online high-yield savings accounts have offered APYs 10–20× higher than traditional bank savings accounts. When comparing:
The future value calculator projects how a specific APY compounds your savings over time. The time value of money calculators provide the complete toolkit for savings and investment analysis.
As compounding frequency n → ∞, the APY formula converges to the continuous compounding limit: APY = e^r − 1, where e = 2.71828... is Euler's number. This is the theoretical maximum APY for any nominal rate. For r = 5%: continuous APY = e^0.05 − 1 = 5.1271%. The difference between daily compounding (5.1267%) and continuous compounding (5.1271%) is 0.0004% — essentially zero for practical purposes. Continuous compounding is primarily used in theoretical finance and option pricing models (Black-Scholes uses continuous compounding) rather than in retail banking products.
The APY formula is: APY = (1 + r/n)n - 1
For continuous compounding: APY = er - 1. The calculator also computes the dollar amount of interest earned on a given deposit over one year to make the difference tangible.
The APY is the true annual return on your deposit, accounting for compounding. The Difference from Nominal Rate quantifies the compounding benefit. Interest Earned shows the actual dollar return on your initial deposit in one year. Balance After 1 Year shows your total account value after one year of compounding.
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Results
$50,000 at 5.15% compounded daily earns $2,642 in one year (APY: 5.28%)
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$25,000 CD at 4.5% compounded quarterly earns $1,144 in one year (APY: 4.58%)
APY (Annual Percentage Yield) is the effective annual return on a deposit account, accounting for compound interest. It tells you exactly how much interest you will earn in one year, expressed as a percentage of the principal.
The interest rate (nominal rate) doesn't account for compounding frequency. APY incorporates compounding, so it's always equal to or higher than the nominal rate. APY provides the true measure of annual return.
Mathematically, yes — they use the same formula: (1 + r/n)^n - 1. APY is the regulatory term used for deposit products (savings, CDs), while EAR is the general financial term. For loans, the corresponding metric is APR.
The Truth in Savings Act (1991) requires banks to disclose APY on deposit products. This standardized metric helps consumers compare offers from different banks that may use different compounding frequencies.
Yes, for the same nominal rate. Daily compounding yields a higher APY than monthly, which yields higher than quarterly, and so on. However, the differences become smaller as frequency increases — the gap between daily and continuous is negligible.
APY varies with market conditions and the Federal Reserve's interest rate policy. In recent high-rate environments, top savings accounts have offered 4-5%+ APY. In low-rate environments, rates can fall below 1%. Always compare to current market averages.
For fixed-rate CDs, yes — the APY is locked for the term. For variable-rate savings accounts and money market accounts, the APY can change at any time as the bank adjusts rates. The advertised APY is the current rate, not a guarantee.
For multi-year investments, the total return is (1 + APY)^years - 1. For example, 5% APY for 10 years gives (1.05)^10 - 1 = 62.89% total return. The APY itself doesn't change; it compounds annually.
A CD ladder involves multiple CDs with staggered maturity dates. Each CD has its own APY based on its term and rate. The blended APY of the ladder is the weighted average of individual CD APYs, but the real benefit is liquidity plus competitive rates.
Real return = APY - inflation rate (approximately). If APY is 5% and inflation is 3%, your real return is about 2%. When APY is less than inflation, your purchasing power actually decreases despite earning interest.
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