APY Calculator
Turn an interest rate (APR) into the APY you really earn, or an APY back into an APR, for any compounding. Then see what a deposit earns and which account pays most.
Enter each account's APR. Your account above is account A.
Accounts side by side
| Account | APR | APY | Fees | Interest | Balance |
|---|
Every compounding choice for your rate
How your APY is worked out
APY = (1 + APR ÷ periods)^periods − 1.
- 1
Rate each period
5% ÷ 12 months= 0.416667%
- 2
Compound for a year
(1 + 0.00416667)^12= 1.051162
- 3
Take away 1
1.051162 − 1= 5.1162% APY
- 4
A year's interest
$10,000.00× 5.1162%= $511.62
Read more: the formula, a worked example, AER and EAR, fees, tax and inflation
The APY (annual percentage yield) is what your money really grows by in a year once interest earns interest. It goes by other names: the AER (annual equivalent rate) in the UK, and the EAR or effective annual rate in finance. The APR, also called the nominal or stated rate, is the yearly rate before compounding. The more often interest is added, the further the APY sits above the APR.
The formula
APY = (1 + APR ÷ periods a year)^(periods a year) − 1
APR = periods a year × ((1 + APY)^(1 ÷ periods a year) − 1)
continuous: APY = e^APR − 1, and APR = ln(1 + APY)
365/360 method: APY = (1 + APR ÷ 360)^365 − 1
balance after the term = deposit × (1 + APY)^years
after-tax APY = APY × (1 − tax rate)
real yield = (1 + after-tax APY) ÷ (1 + inflation) − 1
Worked example
A 5% APR compounded monthly. The rate each month is 5% ÷ 12 = 0.416667%. Over a year, 1 grows to (1 + 0.00416667)12 = 1.051162, so the APY is 1.051162 − 1 = 5.1162%. On a deposit of 10,000 that is 10,000 × 5.1162% = 511.62 of interest in a year, compared with 500.00 if interest were added only once a year.
The other way round: a 5% APY with monthly compounding. 1.051/12 = 1.004074, so the monthly rate is 0.4074% and the APR is 0.004074 × 12 = 4.8889%.
Every compounding choice at 5% APR
| Compounded | APY at 5% APR | APR for 5% APY | Interest on 10,000 |
|---|---|---|---|
| Yearly | 5.0000% | 5.0000% | 500.00 |
| Twice a year | 5.0625% | 4.9390% | 506.25 |
| Quarterly | 5.0945% | 4.9089% | 509.45 |
| Monthly | 5.1162% | 4.8889% | 511.62 |
| Weekly | 5.1246% | 4.8813% | 512.46 |
| Daily (365 or 360-day year) | 5.1267% | 4.8793% | 512.67 |
| Daily, rate ÷ 360 for 365 days | 5.1998% | 4.8125% | 519.98 |
| Continuously | 5.1271% | 4.8790% | 512.71 |
The "365/360" method divides the yearly rate by 360 but adds interest on all 365 days, so it pays a little more. Some banks use it, mostly on loans. Ask which method an account uses if the APY is not shown.
Additions, fees, tax and inflation
Advanced mode grows the deposit one month at a time by (1 + APY)1/12, then adds any monthly amount and takes off any monthly fee. 10,000 at 5% APR compounded monthly with 100 added at the end of every month grows to 11,739.50 in a year. With a fee of 5 a month and no additions, it grows to 10,450.22: the fees of 60 cut the gain from 511.62 to 450.22.
If 30% tax is taken from the interest, the 511.62 becomes 358.13 and the after-tax APY is 5.1162% × 0.7 = 3.5813%. With 3% inflation, the real yield is 1.035813 ÷ 1.03 − 1 = 0.5644% a year: that is how much more your money can really buy. Tax rules differ by country and by account (some savings accounts are tax-free), so enter the rate that applies to you.
Comparing accounts
Compare savings accounts by APY, not APR, because the APY already allows for how often interest is added. A 4.9% APR compounded daily (5.0217% APY) beats a 5% APR compounded yearly (5% APY). A monthly fee can wipe out a better rate on a small balance, so the side-by-side table counts fees too.
Assumes a fixed rate for the whole term. Monthly figures use the equivalent monthly rate, so a bank that credits interest at different times may differ by a few cents. Borrowing APRs in many countries also include some fees, which this calculator does not add.
Common questions
How do I work out APY from APR?
Divide the yearly rate (APR) by the number of times interest is added each year, add 1, raise it to that number, then take away 1. A 5% APR compounded monthly is (1 + 0.05 ÷ 12)^12 − 1 = 5.1162% APY. Compounded daily it is 5.1267%, and compounded continuously e^0.05 − 1 = 5.1271%.
How do I turn an APY back into an APR?
Add 1 to the APY, take the root for the number of periods in a year, take away 1 and multiply by the number of periods. A 5% APY with monthly compounding is 12 × (1.05^(1/12) − 1) = 4.8889% APR.
What is the difference between APR and APY?
The APR (also called the nominal or stated rate) is the yearly rate before compounding. The APY includes the interest earned on interest during the year, so it is the same or higher. Savers should compare accounts by APY; borrowers often see an APR, which on many loans also includes some fees.
Is APY the same as AER or the effective annual rate?
Yes, they measure the same thing: how much 1 grows in a year once compounding is counted. In the UK it is called the AER (annual equivalent rate), and in finance it is often called the EAR or effective annual rate. The formula is the same.
Does daily or monthly compounding make a big difference?
Less than people think. At 5% APR, yearly compounding gives 5.0000% APY, monthly 5.1162%, daily 5.1267% and continuous 5.1271%. On 10,000 for a year that is 500.00, 511.62, 512.67 and 512.71 of interest. A slightly higher rate or a lower fee usually matters more.
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