APY Calculator: Compare Two Accounts Properly

What the APY result shows

APY — annual percentage yield — is what a stated rate is actually worth after a year of compounding. It is always equal to or higher than the nominal rate, and the gap is the compounding.

The line worth noticing is how small that gap is. On a rate around 4%, moving from annual to daily compounding adds roughly nine hundredths of a percentage point. The table below shows every frequency at once for exactly that reason: it demonstrates that frequency is close to a rounding error while the rate is the thing to shop on. A 4.5% account compounded annually beats a 4.25% account compounded daily, every time.

The head-to-head comparison is what APY exists for. Two banks quoting different rates on different compounding bases cannot be compared directly — converting both to APY puts them on one scale, and with a balance entered the difference appears in dollars a year, which is the only form worth making a decision on.

How to use this calculator

Pick a direction. Most of the time you have a rate and want the yield; occasionally an account advertises only APY and you need the underlying rate.
Enter the rate and the compounding frequency from the account disclosure. Most US savings accounts compound daily; CDs vary.
Add your balance to convert the percentages into dollars.
Enter a second rate to compare two offers. The winner is decided on APY, never on the stated rate.

One convention to be aware of: banks quote APY on deposits and APR on loans, and they are not symmetric. APY includes compounding; APR includes fees but, confusingly, does not compound. Comparing a deposit APY against a loan APR is not a like-for-like comparison.

The formula, and why it works

APY = (1 + r ⁄ n)ⁿ − 1

r — the nominal annual rate as a decimal
n — compounding periods per year

Each period earns r/n, and each subsequent period earns on a balance that already includes the last one. Raising the per-period growth to the power of the number of periods is simply the effect of that repetition over a year.

Working backwards inverts it: the nominal rate that produces a given APY is n × ((1 + APY)^1/n − 1). Both directions are exact, which is why this page reports three decimal places — at typical balances the third decimal is worth a few dollars a year, and the difference between two competing offers frequently sits there.

APY assumes the money stays put for a full year and that the rate does not change. On a variable-rate savings account neither is guaranteed, which is why APY is a comparison tool rather than a promise — the savings calculator shows what happens when you are adding to the balance as well.

APY, APR and interest rate

Three terms, routinely confused, and the differences matter.

The interest rate is the raw figure the account or loan is priced at. APY takes a deposit rate and adds the effect of compounding, which makes deposits comparable. APR takes a loan rate and adds most fees, which makes loans comparable — but by convention APR does not include the effect of compounding, so a credit card’s APR understates what a revolving balance actually costs over a year.

Practical consequences. Shop deposits on APY, because it is the only figure that reconciles different compounding. Shop loans on APR, because it is the only figure that includes the fees — and our loan calculator reconstructs the true APR when an origination fee is involved, because a stated rate alone hides it. And when a card quotes 24% APR, the effective annual cost of carrying a balance is higher than 24%, because interest compounds on the balance monthly.

What actually moves the needle

The rate, by a wide margin. A quarter of a point of rate beats any compounding frequency difference on the same money.
Where the money is. The gap between a big-bank savings account and a competitive online one is frequently several percentage points — orders of magnitude more than compounding.
Whether the rate is promotional. An introductory APY that reverts after three months is worth roughly a quarter of what the headline implies. Check the reversion rate, not the teaser.
Tiers and minimums. Some accounts pay the advertised APY only above a balance threshold, or only on the portion within a tier.
Tax. Interest is ordinary income in the year it is credited, so a 4.35% APY nets closer to 3.3% at a 24% marginal rate. That is the figure to compare against a tax-free alternative.

What this calculator assumes

A constant rate for a full year with no deposits or withdrawals. Savings rates are variable and move with the Fed.
No fees or minimum-balance penalties, which some accounts charge and which can exceed the interest on a small balance.
No tax deducted. See above — the after-tax yield is what matters for comparisons against tax-advantaged options.
Standard compounding conventions, using 365 days for daily. A few institutions use 360, which changes the third decimal.

These are planning estimates. The account disclosure is the authority on the rate, the compounding frequency and the conditions attached to it.

One last piece of context worth holding on to. APY is a regulated disclosure precisely because compounding used to be a place where advertised rates could mislead — requiring a single comparable figure removed the incentive to compete on presentation rather than on price. That is why it is worth trusting: it is not a marketing number, it is the one figure a bank is obliged to compute the same way as every competitor. Which is also why an account that leads with anything other than its APY is worth reading twice.

APY questions people ask

Is a higher APY always better?

For a deposit account, yes — that is what APY is designed to tell you, and it already accounts for compounding differences. The things it does not capture are fees, minimum balances, whether the rate is promotional, and how easily you can reach the money.

What is the difference between APY and interest rate?

The interest rate is the stated figure; APY is what that rate is worth after a year of compounding. They are equal only when interest compounds annually. Because the gap depends on the frequency, APY is the only figure that lets you compare two accounts fairly.

Does daily compounding make a big difference?

Less than most people expect. At around 4%, daily rather than annual compounding adds roughly nine hundredths of a percentage point — about $22 a year on $25,000. A quarter-point better rate is worth several times more, which is why the rate is what to shop on.

Why is my credit card APR not an APY?

Convention. APR on lending includes fees but not the effect of compounding, while APY on deposits includes compounding but not fees. A card at 24% APR costs more than 24% a year on a carried balance, because the interest compounds monthly.