APY Calculator
True yearly yield from nominal rate and compounding frequency.
What it does
Banks quote nominal rates while paying APY, and the gap is compounding: interest posted mid year starts earning its own interest. Monthly compounding on five percent nominal pays 5.12% APY, and daily pays a touch more.
The tool above converts any nominal rate with its frequency into APY, yearly dollars per thousand, and the monthly rate.
Frequency matters less than people expect and rate matters more. Moving from monthly to daily compounding adds two basis points at five percent, while half a point of rate adds fifty.
Loan APR mirrors this from the borrower side with fees folded in. Savings shop APY up, loans shop APR down.
How to use
- Enter the nominal rate from the quote.
- Pick the true compounding frequency.
- Compare APY across accounts directly.
- Check minimums and caps that modify the headline.
Formula
- r
- Nominal annual rate as a rate.
- n
- Compounding periods per year.
Continuous compounding caps the ladder at e^r - 1. At 5% that is 5.127%, barely above daily.
Worked example
Example: 5% nominal, monthly compounding
Nominal 5%, posted monthly.
- Monthly rate: 0.05 / 12 = 0.00416667.
- Growth: (1.00416667)^12 = 1.051162.
- APY: 1.051162 - 1 = 5.12%, shown as 5.12%.
- Per $1,000: $51.16 a year.
Reference table
| Compounding | APY | Per $1,000 |
|---|---|---|
| Yearly | 5.00% | $50.00 |
| Quarterly | 5.09% | $50.95 |
| Monthly | 5.12% | $51.16 |
| Daily | 5.13% | $51.27 |
Limits
- Fixed rate assumed. Variable accounts reset.
- Tiered balances pay blended yields.
- Taxes excluded from gross yield.
- Teaser rates expire into lower ones.
Common mistakes
- Comparing nominal rates across frequencies.
- Ignoring balance caps on high yields.
- Missing teaser expirations.
- Forgetting tax on interest.
- Chasing yield into lockups needing the cash.
Try it yourself
Quick checks. Answers sit tucked under each question.
4% nominal, quarterly. APY?
(1.01)^4 - 1 = 4.06%.
$2,000 at 5.12% APY. Yearly?
2 x $51.16 = $102.32.
Questions
APY or nominal: which is higher?
APY, except with yearly compounding where they match.
Why do banks quote nominal?
Regulations require APY disclosure too. Nominal feeds the APY math.
Does compounding frequency matter much?
Little. Rate moves dollars; frequency moves cents.
What is APR then?
Loan yearly cost with fees inside. Higher APR than note rate is normal.
Can APY change?
Yes on variable accounts with markets and policy.
Is APY guaranteed?
Only fixed term products guarantee it. Savings yields float.