APY Calculator

About the APY Calculator

APY exists to settle an argument that interest rates cannot settle on their own.

Two savings accounts. One advertises 4.85%, the other 4.90%. The second is obviously better — except that the first compounds daily and the second compounds once a year, and once you account for that the first one pays more.

That is the whole job of APY: it folds compounding into the rate so that two accounts can be compared as one number against one number.

This calculator works in all three directions — rate to APY, two accounts head to head, and an advertised APY back to the rate behind it.

How to Use the APY Calculator

Pick a mode:

Rate to APY. Enter the advertised interest rate and how often the account compounds. You get the APY and what it pays on your balance.

Compare two accounts. Enter both rates and both compounding frequencies. You get the winner, the margin in percentage points, and the margin in money.

APY back to a rate. Enter an advertised APY and the compounding frequency, and you get the nominal rate behind it — the figure banks almost never publish.

The balance only affects the money figures. APY is a rate and does not depend on how much you have.

How APY Is Calculated

  APY = (1 + r/n)ⁿ − 1

where r is the nominal annual rate and n is the number of compounding periods in a year. On 5% compounded monthly:

  (1 + 0.05/12)¹² − 1 = 0.051162  →  5.12%

The extra 0.12 points is interest earning interest during the year. That is the entire content of the word "effective".

Continuous compounding is not just a very large n. It is the limit as the periods get infinitely short, and it has its own expression:

  APY = e^r − 1
  e^0.05 − 1 = 0.051271  →  5.13%

Entering "365,000 times a year" does not get you there. The limit does.

What Compounding Frequency Is Actually Worth

On £10,000 at a nominal 5%:

Read the bottom of that table carefully. Going from daily to infinitely often is worth four pence a year on ten thousand pounds.

The entire span from annual to continuous is 0.13 percentage points. So the honest rule is: any account paying more than 0.13 points extra in rate wins however either of them compounds. Most competing accounts differ by far more than that.

Note that 0.13 is not a universal figure — it grows with the rate, which is why the calculator works it out for your rate rather than quoting a rule of thumb.

Compare on APY. Shop on rate.

Step-by-Step Example

This is the comparison APY was invented for:

  Account A:  4.85%, compounded daily     →  APY 4.97%
  Account B:  4.90%, compounded annually  →  APY 4.90%

  On 10,000:    496.92   against   490.00

The account advertising the lower rate pays £6.92 more a year. On £50,000 it is £34.60.

Nothing about "4.85" and "4.90" tells you this. You need the APY, and that is precisely why regulators require savings products to quote one.

APY Against APR — The Mistake Everyone Makes

APY is an effective rate. APR is a nominal rate. They are different measures, and they are not comparable.

A 24% credit card APR is 2% a month, and twelve months of 2% compounds to 26.82%. The APR convention divides by twelve and stops there; the APY convention does not.

So:

• A savings account at 5% APY genuinely pays 5% over a year.
• A loan at 5% APR costs more than 5% over a year.

Putting them side by side always flatters the borrowing. If you want a true comparison, convert the APR to its effective rate first — the APR calculator does that — and compare effective against effective.

Working Backwards From an Advertised APY

Invert the formula:

  nominal = n × ((1 + APY)^(1/n) − 1)

A 5% APY compounded monthly comes from a nominal rate of 4.89%. The same 5% APY compounded daily comes from 4.88%.

Two uses for this. First, checking a bank against its own arithmetic — if the rate and the APY they print do not reconcile, something else is going on, often an introductory bonus counted into the headline. Second, comparing against a product elsewhere that quotes a plain rate.

Understanding Your Result

APY is the number to compare accounts on.

What it pays converts the rate into money on your actual balance, which is usually what settles whether a difference is worth the paperwork.

Where it comes from separates the plain interest from the compounding, so you can see how much of the figure each is contributing.

Worth comparing names the full spread that frequency can buy at your rate — the threshold any rate difference has to beat.

Worth knowing is the APY-against-APR warning, because the comparison is so easy to make and always wrong.

When Should You Use This Calculator?

Choosing between savings accounts that quote different rates and compound at different intervals. This is the main event.

Checking an advertised APY. If it does not reconcile with the stated rate and frequency, ask what else is in the number.

Comparing a savings APY against a loan APR. Do not — convert first.

Understanding a fixed-term bond. Some quote gross annual rates, some quote APY, and the difference matters more on multi-year terms.

Sanity-checking a "daily compounding!" claim. Now you can see exactly what it is worth, which is usually a few pounds.

Common Mistakes

Comparing APY to APR. The single most common one. APY includes compounding; APR does not.

Chasing compounding frequency. Worth a tenth of a point at typical rates. The rate is worth several times more.

Assuming APY includes the bonus rate. Introductory rates that drop after twelve months can be folded into a headline figure in ways that are technically correct and practically misleading. Check the rate after the intro period.

Forgetting tax. APY is a gross figure. What you keep depends on your allowances and your tax rate, and that difference dwarfs compounding frequency.

Ignoring inflation. A 5% APY when prices rise 4% is a real return near 1%. The savings calculator handles that side.

Assuming the rate is fixed. Most easy-access accounts can change their rate whenever they like. An APY is a snapshot, not a promise.

Every figure here is an estimate for planning. Product terms vary, and this is not financial advice.