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APY Calculator

Enter a nominal annual rate and a compounding frequency. The calculator returns the APY (annual percentage yield), shows how much higher it is than the stated rate, and applies it to a starting balance to estimate first-year interest.

%

The stated annual rate before compounding effects. · e.g. 5

Compounding frequency

$

See first-year interest at this APY. · e.g. 10,000

Same rate at different compounding frequencies

  • Annually5%
  • Semi-annually5.0625%
  • Quarterly5.0945%
  • Monthly5.1162%
  • Daily5.1267%
  • Continuously5.1271%
Annual percentage yield (APY)

APY

5.1162%

Effective annual rate. 0.1162% higher than the nominal 5% due to compounding.

Nominal rate5%
Effective annual yield5.1162%
Compounding boost0.1162%
Starting balance$10,000.00
First-year interest$511.62
Balance after one year$10,511.62

Estimate only. Real accounts can have fees, tiered rates, promotional periods, and minimum balance rules that change the effective yield.

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Examples

5% nominal · monthly compounding

APY ≈ 5.1162%

5% nominal · daily compounding

APY ≈ 5.1267%

5% nominal · continuous compounding

APY ≈ 5.1271%

5% nominal · annual compounding

APY = 5.0000%

How it works

The APY formula converts a nominal interest rate plus a compounding frequency into the effective annual rate. The more often interest is added to the balance, the more interest earns interest before the year is over, and the higher the APY.

APY (discrete compounding)

APY = (1 + r/n)^n − 1

The parts

  • APY = effective annual yield (decimal)
  • r = nominal annual rate (decimal)
  • n = compounding periods per year

Continuous compounding

APY = e^r − 1

First-year interest on a starting balance

interest = balance × APY

Multiply your starting balance by the APY (as a decimal) to estimate how much interest the account earns in one year.

What APY tells you

APY is the real one-year return you get from a deposit account or fixed-rate product, after compounding has done its work. It is the number to compare between accounts because it neutralizes differences in compounding frequency. Two accounts at the same APY produce the same first-year interest on the same balance, regardless of how often they compound.

How the calculator works

You enter a nominal annual rate and pick a compounding frequency (annually, semi-annually, quarterly, monthly, daily, or continuously). The calculator returns the APY, the gap between APY and the nominal rate (the compounding boost), and the first-year interest on the optional starting balance. A short table shows the APY you would get at the same nominal rate for every frequency option, so you can see at a glance how much compounding matters.

APY vs APR

APR is the nominal annual rate without compounding effects. APY is the effective annual rate with compounding included. For savings products, you usually want APY. For loans, you usually see APR. When comparing a loan APR to a savings APY, remember that they are measuring different things.

For loan math itself, the loan calculator and mortgage calculator handle the amortization side of compound interest.

Why APY can be higher than the stated rate

When interest is compounded more than once a year, each compounding period adds interest to the balance, and the next period earns interest on that new, larger balance. The result is that the effective rate is a bit higher than the nominal rate. A 5% nominal rate compounded monthly produces an APY of about 5.1162%, because the extra 0.1162 percentage points come from interest earning interest during the year.

Worked example

Nominal rate 5%, monthly compounding, starting balance $10,000.

  • Convert nominal rate to decimal: 5% = 0.05
  • Apply APY formula: (1 + 0.05 / 12)^12 − 1 ≈ 0.05116
  • Convert to percent: 5.1162%
  • First-year interest on $10,000: 10,000 × 0.05116 ≈ $511.62
  • Balance after one year: ≈ $10,511.62

The same 5% nominal rate produces an APY of exactly 5.0000% with annual compounding, about 5.0945% with quarterly, 5.1267% with daily, and 5.1271% with continuous. The calculator shows the full table side by side.

Where APY shows up

APY is the headline number for savings products: savings accounts, money market accounts, and certificates of deposit (CDs) advertise APY because it is the easiest fair comparison. APY also shows up on bond funds, treasury products, and some checking accounts. For projecting how a balance grows over many years, the compound interest calculator takes APY-style math out to a longer horizon with optional monthly contributions.

Common mistakes

  • Comparing two products by nominal rate when they compound differently. Convert both to APY first.
  • Confusing APR with APY. APR is nominal; APY is effective. On a savings product, APY is the one to use.
  • Assuming that going from daily to continuous compounding will boost the return noticeably. The difference is fractions of a percent.
  • Treating a promotional APY as permanent. Many high-yield accounts revert to a lower rate after a promo window or require a minimum balance to keep the rate.
  • Ignoring fees and minimum-balance penalties. They can erase the compounding boost entirely.

Related tools

Disclaimer. This calculator is an estimate for general planning. Actual returns can vary based on fees, tiered rates, promotional periods, balance minimums, taxes, and account rules. It is not investment, tax, or financial advice, and it does not guarantee any return.

Frequently asked questions

APY (annual percentage yield) is the effective annual rate of interest after compounding is taken into account. It tells you the real growth of a balance over one year for a given nominal rate and compounding frequency. APY is the number to compare when you are shopping savings accounts, certificates of deposit, or any product that pays compound interest.

Use APY = (1 + r/n)^n − 1, where r is the nominal annual rate as a decimal and n is the number of compounding periods per year. For continuous compounding, APY = e^r − 1. For example, a 5% nominal rate compounded monthly gives APY = (1 + 0.05/12)^12 − 1 ≈ 0.05116, or about 5.1162%.

APR (annual percentage rate) is the nominal annual rate. APY (annual percentage yield) is the effective rate after compounding. On loans, lenders often quote APR, which understates how much you actually pay if interest compounds inside the year. On savings, banks usually quote APY, which is the more honest measure of how much you actually earn.

The interest rate (also called the nominal rate) is what gets quoted before compounding. APY is the effective rate after one year of compounding at that nominal rate. Because compounding lets interest earn interest, APY is always at least as high as the nominal rate, and it is higher when compounding happens more than once a year.

Higher compounding frequency produces a slightly higher APY at the same nominal rate. Going from annual to monthly compounding makes a noticeable jump; going from daily to continuous makes almost no difference. For example, at a 5% nominal rate, APY is exactly 5% with annual compounding, about 5.0945% with quarterly, about 5.1162% with monthly, about 5.1267% with daily, and about 5.1271% with continuous compounding.

Continuous compounding is the mathematical limit where interest compounds an infinite number of times per year. The formula is APY = e^r − 1, where e ≈ 2.71828 is Euler's number. In practice, continuous compounding is rare in retail products; it is most often used in derivatives and academic finance. For real-world consumer products, daily compounding is essentially identical.

Because interest paid during the year starts earning more interest before the year is over. A 12% nominal rate compounded monthly pays 1% in month one, then 1% on the slightly larger balance in month two, and so on. By the end of the year you have earned a bit more than 12% on the original balance. That bit more is the compounding boost.

No, not for normal positive rates. APY equals the nominal rate when compounding is exactly annual, and exceeds it for any more frequent compounding. APY is never lower than the nominal rate at the same nominal r.

Savings accounts, certificates of deposit (CDs), money market accounts, and bond funds all advertise APY. So do some checking accounts and treasury products. When you compare two savings accounts, compare their APYs, not their nominal rates, because their compounding frequencies might differ.

Not directly. It shows the first-year interest at the computed APY. To project compound growth over multiple years, use the compound interest calculator, which accepts a time horizon and optional monthly contributions.

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