APY Calculator
Effective annual yield from a nominal rate
🔒 Client-side · Method · · Disclaimer · APY Calculator
APY Calculator turns the numbers behind effective annual yield from a nominal rate into a result, step by step. Enter Nominal Rate (%), Principal ($) and Years in any order — APY recalculates on every edit. APY ties each output to its formula. Students and professionals reach for APY when speed matters. You can disconnect once APY has loaded; the arithmetic runs locally. APY handles apy calculator annual percentage yield compounding the same way as related figures — one of the Finance tools on CalcProMaster. APY goes from question to answer fast. Open APY and enter your numbers.
What APY means, in one number
APY is the rate you actually earn after compounding, expressed annually. A 5% nominal rate compounded monthly produces 5.116% APY: on $10,000 that is $511.62 of interest in a year, not $500.
It exists so accounts with different compounding schedules can be compared on one line. The nominal rate alone cannot do that.
The APY formula
APY = (1 + Nominal rate ÷ Compounding periods)Periods − 1
A 5% nominal rate compounded monthly: (1 + 0.05 ÷ 12)12 − 1 = 5.116%.
| Nominal rate | Monthly | Daily | Annual |
|---|---|---|---|
| 4.00% | 4.074% | 4.081% | 4.000% |
| 5.00% | 5.116% | 5.127% | 5.000% |
| 6.00% | 6.168% | 6.183% | 6.000% |
What a given APY actually earns on $10,000
Once a rate is quoted as APY, the compounding is already inside it, so the one-year interest is a single multiplication: balance × APY. That is why APY is the number to compare advertisements with and the nominal rate is not.
| APY | Interest on $10,000 for one year | Balance after a year | Monthly rate that produces it |
|---|---|---|---|
| 3.00% | $300 | $10,300 | 0.2466% |
| 3.50% | $350 | $10,350 | 0.2871% |
| 4.00% | $400 | $10,400 | 0.3274% |
| 4.10% | $410 | $10,410 | 0.3354% |
| 4.50% | $450 | $10,450 | 0.3675% |
| 5.00% | $500 | $10,500 | 0.4074% |
For any other balance, scale the row: 5.00% APY on $1,000 is $50, and on $100,000 it is $5,000. The last column matters when you check a statement — a bank that credits interest monthly does not pay APY ÷ 12 each month, it pays (1 + APY)1/12 − 1, the smaller figure in that column. Over a full year the two routes meet exactly at the APY.
APY, AER and APR — same number or different?
The label changes with the country, not the arithmetic. What this page calls APY is the standard US disclosure for deposit accounts; in the UK and Ireland the same compounded figure is quoted as AER (annual equivalent rate), and deposit rates in Australia and Canada are also quoted on an effective annual basis. A 5% nominal rate compounded monthly is 5.116% APY and 5.12% AER — one number, two names, which is what makes savings rates from different countries comparable once both are quoted this way.
APR is not interchangeable with APY. APR describes borrowing, and a lending APR can include fees on top of the compounding, so a savings APY and a loan APR are built differently. Compare deposit accounts on APY (or AER) and borrowing on APR.
More frequent compounding means a higher APY for the same nominal rate. Related: compound interest and finance guides.
What a monthly contribution earns
The calculator above compounds a single balance. Most savings plans also add money every month, and the same rate covers both cases. With deposits going in at the end of each month and interest credited monthly at the rate the APY implies — i = (1 + APY)1/12 − 1 — the balance after n months is:
Balance = Deposit × ((1 + i)n − 1) ÷ i
At 5.00% APY, i is 0.4074% a month. Paying in $1,000 at the end of every month for a year builds $12,272.58: $12,000 of your own deposits plus $272.58 of interest.
| APY | Balance after 12 months at $1,000/mo | Interest earned | Balance after 24 months | Interest earned |
|---|---|---|---|---|
| 3.00% | $12,164.12 | $164.12 | $24,693.16 | $693.16 |
| 4.00% | $12,218.44 | $218.44 | $24,925.62 | $925.62 |
| 5.00% | $12,272.58 | $272.58 | $25,158.78 | $1,158.78 |
The same $12,000 parked as a lump sum for a year at 5.00% APY ends at $12,600.00 — $327.42 more than the monthly route. That gap is not a fee or a penalty: it is the interest the money earned during the months it would not yet have been deposited, which is why a savings projection is only comparable next to the deposit schedule it assumes.
APY and APR, side by side
Deposits and loans run on the same compounding arithmetic; what differs is the label — and, on the borrowing side, whether fees sit inside the number. The two rows below are one rate written both ways:
| Quoted as | Arithmetic | The other label |
|---|---|---|
| 5.000% nominal, compounded monthly | (1 + 0.05 ÷ 12)12 − 1 | = 5.116% effective — the APY, and the AER in the UK and Ireland |
| 4.889% nominal, compounded monthly | 12 × ((1.05)1/12 − 1) | = 5.000% effective |
Read the first row backwards and it becomes the second: a 5.000% effective rate is a 4.889% monthly-compounded nominal rate, and both describe the same account. On the deposit side the effective figure is what gets advertised as APY. On the borrowing side an APR can also carry fees on top of that compounding — once fees are inside the number the two stop matching, and the APR is no longer the same maths relabelled. That is the whole difference, and it is why a savings APY and a loan APR are two different constructions rather than two names for one rate.
One caution the arithmetic cannot fix: a promotional APY applies only while the promotion runs. Every table on this page assumes the rate holds for the whole period, so treat a rate that reverts as a shorter period at a lower rate, and re-run the numbers when it changes.
The formula
APY = (1 + r ÷ m)^m − 1, where r is the nominal annual rate as a decimal and m is the number of compounding periods per year. Monthly is m = 12, daily is 365, quarterly is 4.
The gap between APY and the nominal rate grows with both the rate and the frequency: at 5% monthly it is 0.116 points; at 5% daily it is about 0.127; at 12% monthly it is 0.186.
Worked example
r = 5% = 0.05, m = 12. Monthly rate = 0.05 ÷ 12 = 0.0041667. (1.0041667)^12 = 1.051162, so APY = 5.116%.
Future value = $10,000 × 1.051162 = $10,511.62, which is $511.62 of interest. Over one year the compounding adds $11.62 to the $500 a simple-rate account would pay.
Why the frequency still matters
The difference between monthly and daily compounding at 5% is $11 a year on $10,000 — real, but smaller than the difference between two accounts quoting 5.00% and 5.15%. When comparing, check the APY first, the nominal rate second, and the compounding frequency only to explain a gap.
Over several years the gap compounds on itself. At 5.116% for ten years, $10,000 becomes about $16,470; at a 5.00% simple rate it would be $15,000-ish depending on how interest is credited. The page's years field multiplies the exponent, so you can see that directly.
Where APY misleads
- It assumes the rate holds. Variable accounts reprice, and a headline APY is a snapshot, not a contract.
- It ignores fees. A monthly maintenance fee can wipe out the compounding advantage entirely.
- It is not for loans. On borrowing, the equivalent comparison is APR, which includes fees — using APY there understates the cost.
- Promotional tiers. Some APYs apply only to the first $2,000 of balance; the effective yield on a larger deposit is lower.
Common input errors
- Entering 0.05 for a 5% rate. The field expects percent, so 0.05 returns an APY of 0.05%, not 5%.
- Choosing annual compounding when the account credits monthly. That understates the APY by the whole compounding effect.
- Reading the APY as the total return over the term. It is an annualised rate; over five years the multiplier is (1+APY)^5, not 5 × APY.
Frequently Asked Questions
Why is 5% compounded monthly 5.116% and not 5%?
Because interest is credited twelve times and each credit earns interest afterwards. (1 + 0.05/12)^12 − 1 = 0.051162, so the effective annual yield is 5.116%.
Is daily compounding much better than monthly?
At 5% the difference is about one basis point — 5.127% versus 5.116%. It matters at high rates and long horizons, but it is not why one account beats another.
How much interest does $10,000 earn in a year at 5% APY?
$511.62, because the APY already includes compounding. At a nominal 5% compounded monthly the balance ends at $10,511.62; a simple 5% would pay $500.
Should I compare savings accounts by APY or by rate?
By APY — it is the only figure that already accounts for compounding frequency. Then check fees and balance tiers, because those are outside the APY.
Does APY work for loans and credit cards?
No. Borrowing uses APR, which folds in fees and is calculated differently. An APY figure on a loan understates the real cost, so compare like with like.
Sortino Ratio Calculator and other Finance tools
Sortino Ratio Calculator · Position Size Calculator · EV/EBITDA Calculator · Quarterly Estimated Tax Calculator · Required Minimum Distribution Calculator · Roommate Rent Split Calculator · Finance Guides