Calculate the annual percentage yield (APY) from an interest rate and its compounding frequency, using APY = (1 + r/n)n − 1. APY shows the real return once compounding is included, so it is the fairest way to compare savings accounts and CDs. Optionally add an initial deposit and term to see the final balance and interest earned. You can also work in reverse — leave the rate blank and enter an APY.
The APY calculator works out the annual percentage yield of a savings account, certificate of deposit, or any interest-bearing investment. APY is the single most useful number for comparing where to keep your money, because it captures not just the stated interest rate but also the effect of compounding — the way interest earns interest over the year. Enter the interest rate and how often it compounds, and the calculator returns the APY instantly. Add an initial deposit and a term, and it also shows the final balance and the interest you would earn. It even works in reverse, finding the interest rate that produces a given APY.
If you have ever compared two savings accounts and wondered why the one with the "lower" rate actually pays more, the answer is almost always compounding frequency, and APY is what makes that difference visible. This page explains what APY is, how it differs from a plain interest rate, the formula behind it, worked examples you can reproduce, and answers to the questions people ask most.
APY (annual percentage yield) is the effective annual rate of return on an investment, taking compound interest into account. It tells you the real percentage your balance will grow over one year, assuming you leave the money and its interest untouched. Because it folds compounding into a single figure, APY lets you compare accounts fairly even when they compound at different frequencies.
The key insight is that money can earn interest more than once a year. If an account pays 2% and compounds every six months, you do not simply get 2% at year end. Instead you get 1% after six months, and then the second 1% is applied to the slightly larger balance — so you end up with a little more than 2%. That "little more" is exactly what APY measures. The more frequently interest compounds, the higher the APY climbs above the stated rate.
People often use "interest rate," "APR," and "APY" loosely, but they are not the same:
APY is always greater than or equal to the nominal rate. They are equal only when interest compounds just once a year; for any more frequent compounding, the APY is higher. This is why financial institutions are generally required to advertise APY for savings products — it is the honest, comparable number. When you shop for a high-yield savings account or a CD, compare the APYs, not the raw interest rates.
The formula for annual percentage yield is:
APY = (1 + r/n)n − 1
where r is the nominal annual interest rate (as a decimal) and n is the number of times interest compounds per year. To express the result as a percentage, multiply by 100. In words: divide the annual rate by the number of compounding periods, add one, raise the whole thing to the power of the number of periods, and subtract one.
Common values of n are: 1 for yearly, 2 for half-yearly (semi-annual), 4 for quarterly, 12 for monthly, 52 for weekly, and 365 for daily compounding.
With r = 0.02 and n = 2:
APY = (1 + 0.02/2)2 − 1 = (1.01)2 − 1 = 0.0201 = 2.01%
So a 2% rate compounded twice a year yields 2.01% — slightly more than the stated 2%. These are the calculator's default values, so you can press Calculate to see it, along with the final balance on a $1,000 deposit ($1,020.10) after one year.
With r = 0.007 and n = 4:
APY = (1 + 0.007/4)4 − 1 ≈ 0.00702 = 0.702%
Here a 0.7% rate compounded quarterly gives an APY of about 0.702%. The uplift is tiny at low rates, but at higher rates and more frequent compounding it becomes meaningful.
The more often interest compounds, the more interest-on-interest you earn, and the higher the APY. To see the effect clearly, consider a 5% nominal rate at different frequencies:
Notice the gains get smaller as frequency increases — the jump from yearly to monthly is far bigger than from monthly to daily. As compounding approaches "continuous," the APY approaches a ceiling of er − 1, which for 5% is about 5.127%. In practice, the difference between daily and continuous compounding is negligible, so daily-compounding accounts already capture almost all of the possible benefit.
Once you know the APY, finding how much a deposit grows is straightforward. Over a whole number of years, the final balance is:
Final balance = deposit × (1 + APY)term
For example, $1,000 at a 2.01% APY for one year grows to $1,000 × 1.0201 = $1,020.10, earning $20.10 in interest. Over longer terms the growth compounds year on year: the same account over 5 years would reach about $1,000 × 1.02015 ≈ $1,104.60. The calculator does this for you whenever you enter both an initial deposit and a term, showing the final balance and the total interest earned.
Sometimes you know the APY an account advertises and want to find the underlying nominal rate — for instance, to compare it with a product quoted as a plain interest rate. The relationship can be rearranged:
r = n × ((1 + APY)1/n − 1)
Leave the interest-rate field blank, enter the APY, choose the compounding frequency, and the calculator returns the nominal rate. This is handy for converting between how different banks quote their products so you are always comparing like with like.
APY is the great equalizer of savings shopping. Two accounts can advertise the same interest rate yet pay different amounts because one compounds daily and the other annually. Conversely, an account with a slightly lower nominal rate but more frequent compounding can out-earn one with a higher rate that compounds once a year. Because APY bakes compounding into a single number, it removes the guesswork: the account with the higher APY pays more, full stop (assuming no fees). This is why regulators require APY disclosure on deposit accounts, and why it should be the first number you check.
APY is the yield you earn; APR (annual percentage rate) is most often the cost you pay on loans and credit cards, and it typically excludes the effect of compounding (though it may include fees). On the saving side, more frequent compounding is good for you and pushes APY up. On the borrowing side, more frequent compounding works against you, making the effective cost higher than the stated APR. When you are the saver, chase a high APY; when you are the borrower, look for a low APR and check how often interest is compounded, because that determines your true cost.
APY captures one year of compounding, but its real magic shows over many years. Because each year's interest is added to the principal and then earns interest itself, balances grow exponentially rather than linearly. A modest-looking APY, sustained over decades, can more than double your money through compounding alone. That is why starting early and leaving money to compound is such powerful advice for savers, and why even small differences in APY matter more the longer you save. The APY figure this calculator produces is the annual building block of that long-term growth — feed it into the final-balance calculation with a longer term to see how dramatically it accumulates.
APY tells you how fast your balance grows in nominal terms, but it does not account for inflation — the gradual rise in prices that erodes the purchasing power of money. To understand what your savings are really worth, compare your APY with the inflation rate. If an account pays a 3% APY while inflation runs at 2%, your real return is roughly 1% — your money grows, but only a little in terms of what it can actually buy. When inflation is higher than your APY, your balance still increases in dollars, yet its real value shrinks. This is why savers often seek out high-yield accounts during inflationary periods: a competitive APY is the first line of defense in keeping savings ahead of rising prices. Taxes matter too — interest earned is usually taxable, so your after-tax, after-inflation return can be noticeably lower than the headline APY. The calculator shows the gross APY; keep inflation and taxes in mind when judging whether a given yield truly grows your wealth.
Not every advertised APY is permanent. A fixed APY, common on certificates of deposit, is locked in for the full term, so you know exactly what you will earn regardless of what happens to interest rates. A variable APY, typical of savings and money market accounts, can change at any time as the bank adjusts its rate in response to the wider market. That means the enticing APY you open an account with may drop weeks later, or rise if rates climb. When comparing accounts, check whether the APY is fixed or variable, and for variable accounts consider the bank's track record of keeping rates competitive. The APY this calculator computes reflects the rate you enter; if your real-world rate changes, simply recalculate with the new figure to see the updated yield and balance.
Before standardized APY disclosure, comparing savings accounts was genuinely confusing, because banks could quote rates using different compounding assumptions that made products look better than they were. In the United States, the Truth in Savings Act of 1991 required financial institutions to advertise the annual percentage yield using a uniform formula, so consumers could finally compare accounts on an equal footing. That is why APY is now the standard headline number on savings products worldwide, and why understanding it — and being able to compute it yourself with a tool like this — puts you on a level playing field with the institutions competing for your deposit.
The interest rate is the stated annual rate before compounding. APY is the effective rate after compounding, so it reflects what you actually earn in a year. APY is always equal to or higher than the nominal rate.
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. Multiply by 100 to get a percentage.
Yes, for the same nominal rate, more frequent compounding produces a higher APY. The gains shrink as frequency increases, approaching a limit at continuous compounding (er − 1).
Yes, assuming no fees and equal safety. A higher APY means a higher real return, so among comparable, fee-free accounts the one with the highest APY pays the most.
Yes. Leave the interest-rate field blank and enter the APY; the calculator solves r = n × ((1 + APY)1/n − 1) for your chosen compounding frequency.
APY = (1 + 0.02/12)12 − 1 ≈ 2.018%. Monthly compounding raises the 2% nominal rate to just over 2.01%.
This APY Calculator is provided for general educational and informational purposes. It uses the standard APY formula and assumes a constant rate and regular compounding with no fees or taxes. Actual account yields may differ; always check the terms and disclosures of a specific financial product.