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Optional. Used for future value calculation.
%
Enter the advertised interest rate (APR).
How often interest is added to the balance.
yrs
Optional. Defaults to 1 year if left blank.
Enter a nominal rate and press Calculate.
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About

A nominal interest rate advertised by a bank does not reflect actual earnings. Compounding frequency changes the effective return. A 5% rate compounded daily yields more than the same rate compounded annually. The difference compounds over time and can amount to hundreds or thousands of dollars on large deposits. Failing to compare APY across products means leaving money on the table. This calculator converts any nominal rate and compounding schedule into the standardized Annual Percentage Yield (APY), computed as APY = (1 + rn)n 1, following the Federal Truth in Savings Act (Regulation DD) methodology.

The tool assumes a fixed nominal rate over the entire period. It does not account for variable-rate products, fees, or early withdrawal penalties. For tiered-rate accounts, calculate each tier separately. Pro tip: always compare APY rather than nominal rate when evaluating certificates of deposit or high-yield savings accounts - it is the only apples-to-apples metric.

apy calculator annual percentage yield compound interest savings calculator interest rate comparison compounding frequency future value calculator

Formulas

The Annual Percentage Yield represents the real rate of return on a deposit after accounting for the effect of compounding within a year.

APY = (1 + rn)n 1

Where r = nominal annual interest rate (as a decimal), and n = number of compounding periods per year.

For continuous compounding, the limit as n yields:

APYcont = er 1

Future value of a deposit over t years:

FV = P × (1 + rn)n × t

Total interest earned:

I = FV P

Where P = initial principal (deposit amount), t = number of years, FV = future value, and I = total interest earned. The constant e 2.71828 is Euler's number.

Reference Data

Nominal RateCompounded AnnuallyCompounded QuarterlyCompounded MonthlyCompounded DailyCompounded Continuously
1.00%1.0000%1.0038%1.0046%1.0050%1.0050%
2.00%2.0000%2.0151%2.0184%2.0201%2.0201%
3.00%3.0000%3.0339%3.0416%3.0453%3.0455%
4.00%4.0000%4.0604%4.0742%4.0808%4.0811%
5.00%5.0000%5.0945%5.1162%5.1267%5.1271%
6.00%6.0000%6.1364%6.1678%6.1831%6.1837%
7.00%7.0000%7.1859%7.2290%7.2501%7.2508%
8.00%8.0000%8.2432%8.3000%8.3278%8.3287%
9.00%9.0000%9.3083%9.3807%9.4162%9.4174%
10.00%10.0000%10.3813%10.4713%10.5156%10.5171%
12.00%12.0000%12.5509%12.6825%12.7475%12.7497%
15.00%15.0000%15.8650%16.0755%16.1798%16.1834%
18.00%18.0000%19.2519%19.5618%19.7164%19.7217%
20.00%20.0000%21.5506%21.9391%22.1336%22.1403%
25.00%25.0000%27.4429%28.0732%28.3916%28.4025%

Frequently Asked Questions

More frequent compounding means interest accrues on previously earned interest sooner. A 5% nominal rate compounded daily produces an APY of approximately 5.1267%, while the same rate compounded annually yields exactly 5.0000%. The gap widens as the nominal rate increases. At 20% nominal, the difference between annual and daily compounding exceeds 2.13 percentage points.
APR (Annual Percentage Rate) is the nominal rate without compounding effects. APY includes compounding. For loans, APR is typically quoted because it excludes compounding of interest on unpaid balances. For savings, APY is mandated by the Truth in Savings Act (Regulation DD) because it reflects actual earnings. If a bank quotes 4.80% APR compounded monthly, the APY is 4.907%. Always compare APY to APY across products.
The difference is marginal. Continuous compounding uses APY = er 1, while daily uses n = 365. At a 10% nominal rate, daily compounding gives 10.5156% APY versus 10.5171% for continuous - a difference of 0.0015 percentage points. On a $100,000 deposit over one year, that equals roughly $1.50.
APY is an annualized metric, but its impact multiplies over time due to compound growth. A 5.12% APY on $10,000 earns $512 in year one. Over 10 years, the same deposit grows to approximately $16,470 - earning $6,470 total, not $5,120. The extra $1,350 is compound interest on interest.
APY becomes negative when the nominal rate is negative, which occurs in some central bank policies (e.g., European Central Bank negative deposit facility rates). A nominal rate of −0.50% compounded monthly produces an APY of approximately −0.4994%. This means the deposit loses value over time. The calculator handles negative rates correctly.
Banks may use actual day counts (365 or 366 for leap years) rather than idealized compounding periods. Some use the ACT/365 day-count convention. Introductory or tiered rates also affect quoted APY. This calculator assumes a fixed nominal rate over the entire period with uniform compounding intervals. For exact figures matching a specific product, consult the institution's disclosure documents.