APY Calculator
What a quoted rate is really worth once the compounding is counted.
Details
APY
4.594%
4.5% compounded monthly is worth 0.094% more
This turns a quoted interest rate into its annual percentage yield — the figure that already counts the compounding, and the only one that lets you compare two savings accounts fairly.
Add a balance and a term and it also shows what that yield actually pays you, in money rather than percentages.
What is APY?
APY is the annual percentage yield: what a rate is really worth over a year once the compounding is counted. A bank that pays 4.5% and adds the interest monthly is not paying you 4.5%. It is paying you 4.594%, because the interest added in January earns interest for the eleven months after it.
That gap is why the number exists. A nominal rate on its own cannot be compared between banks, because two accounts can quote the same rate and credit it at different intervals. In the United States the Truth in Savings Act requires deposit accounts to disclose APY for this reason, so it is the figure on the advert and the figure to compare.
APY and APR are opposites in one important way. APY is what you earn and it includes compounding. APR is what you pay on borrowing, and it deliberately excludes compounding. Comparing one against the other will always flatter the loan.
What to enter
- Interest rate
- The rate as quoted. If the bank calls it a nominal rate or just 'interest rate', enter it here and pick how often it compounds. If the bank already calls it APY, enter it and leave compounding on Annually — the answer comes back unchanged, which is correct.
- Compounding
- How often interest is added to the balance. More often means a higher yield from the same rate, though the gains shrink quickly.
- Starting balance
- What you have in the account. Only affects the money figures, never the yield itself.
- How long
- How long the money stays put. The yield is annual regardless; this is what turns it into a total.
What this assumes
The rate stays the same for the whole term. Savings rates are variable in practice and banks can change them at any time; a CD is the usual exception.
Nothing is added or withdrawn. To model regular deposits, use the savings calculator instead.
Interest is left in the account to compound. Withdrawing it as it is paid gives you the nominal rate, not the yield.
No tax is deducted. Interest on a normal savings account is taxable income in the year it is credited.
How to calculate APY
The formula is short, and the whole of it is in the exponent. Everything APY does comes from the fact that interest already paid starts earning on its own.
- r
- The nominal annual rate, as a decimal
- n
- How many times a year interest compounds
Turn the rate into a decimal. Divide the quoted percentage by 100. A 4.5% rate becomes 0.045.
Split it across the periods. Divide by the number of times a year interest is added. Monthly means 0.045 / 12 = 0.00375, which is what each month actually pays.
Compound it for a full year. Add 1 and raise it to the number of periods. That is the balance after a year for every $1 you started with.
Take the $1 back out. Subtract 1 to leave the growth on its own, then multiply by 100 to read it as a percentage.
See a worked example: 4.5% compounded monthly
- Nominal rate
- 4.5% a year
- Compounding
- Monthly, so 12 periods
As a decimal: 0.045.
Per month: 0.045 / 12 = 0.00375.
After twelve months: (1.00375) to the power of 12 = 1.04594.
Subtract the original dollar: 1.04594 − 1 = 0.04594.
On a $10,000 balance that is $459.40 in the first year, not the $450 the headline rate suggests.
APY: 4.594%
Frequently asked questions
- What's 4% APY on $10,000?
$400 in the first year. APY already includes the compounding, so no further adjustment is needed — 4% of $10,000 is the answer, whatever interval the bank actually credits it at.
Left alone it accelerates, because the interest earns too. After five years the balance is $12,166.53, and after ten it is $14,802.44.
- What is 5% APY on $1,000?
$50 in the first year, for the same reason: the yield is the figure after compounding, so you multiply it straight against the balance.
Scaling is direct. $5,000 earns $250, $10,000 earns $500. Doubling the balance doubles the interest, since nothing in the formula depends on how much you have.
- How do you calculate APY per month?
There is no monthly APY — the Y is 'yearly', and quoting a monthly one would be a contradiction. What people usually want is either the monthly interest, or the yield a monthly rate produces.
For the monthly interest, take the balance times the APY and divide by 12. For the yield from a monthly rate: APY = (1 + r/12)¹² − 1, so 4.5% compounded monthly gives 4.594%.
- Is 3.5% APY good?
It depends entirely on what rates are doing, which is why no honest page gives a fixed answer. Compare it against what high-yield accounts are paying that week, not against a number from an article.
The more useful test is against inflation. A yield below the inflation rate means the balance grows while its purchasing power shrinks, which is the thing worth noticing rather than whether a figure sounds high.
- What is the difference between APY and interest rate?
The interest rate is what the bank quotes before compounding. APY is what it comes to after a year of that compounding being added back in. They are identical only when interest compounds once a year.
The gap widens with the rate. At 1% the difference between annual and monthly compounding is half a basis point; at 10% it is nearly half a percentage point.
- What is the difference between APY and APR?
APY is what you earn; APR is what you pay. APY includes the effect of compounding. APR is a borrowing figure and deliberately leaves compounding out, though it does fold in some fees.
The practical consequence is that they are not comparable. A 6% APR loan costs more than 6% a year if it compounds monthly, while a 6% APY account pays exactly 6%.
- Can APY change after I open the account?
On an ordinary savings or money market account, yes, at any time and usually without much notice. The rate follows what the Federal Reserve is doing, so it falls when rates fall.
A certificate of deposit is the exception: the yield is fixed for the term, which is what you are being paid for giving up access to the money. Introductory or promotional rates on savings accounts almost always revert.
Problems people actually run into
Comparing a nominal rate against an APY
One bank advertises 4.55% and another advertises 4.594% APY. They look like different offers and may be the same one — the first quoting a nominal rate compounded monthly, the second quoting the yield that comes out of it.
Check which number each bank is giving you before comparing. Deposit accounts in the US are required to disclose APY, so if a figure is not labelled, ask what it compounds at.
Chasing daily compounding
Daily compounding is marketed as though it changes the outcome. At 5% it beats monthly by about a hundredth of a percentage point — $1.06 a year on a $10,000 balance.
The rate is what matters, by a wide margin. An account paying 4.75% compounded annually beats one paying 4.5% compounded daily, every time.
Assuming the rate will hold
This projects forward at a fixed yield, and a savings rate is not fixed. Banks move them when the Federal Reserve moves, and an introductory rate often drops after a few months.
Treat anything beyond a year as an illustration rather than a forecast. A CD is the version of this that genuinely locks, which is what you are giving up access to the money for.
Forgetting the tax
Interest in an ordinary savings account is taxable in the year it is credited, and the bank reports it. The figures here are all before tax.
The yield you keep is lower than the yield you are quoted, by whatever your marginal rate is. Tax-advantaged accounts are the exception and are worth checking before chasing a few basis points elsewhere.
Results are estimates for general information only and are not professional financial, medical, or legal advice. Read our full disclaimer.
Sources
- Annual Percentage Yield Calculation Tool · Federal Financial Institutions Examination Council
- 12 CFR Part 1030 — Truth in Savings (Regulation DD), which sets the APY formula and requires its disclosure · Electronic Code of Federal Regulations
- Deposit Insurance — what is covered if a bank fails · Federal Deposit Insurance Corporation
Last updated: September 20, 2026
