APY Calculator

What APY Tells You

A bank might advertise “5% a year,” but if it pays that interest monthly, the interest starts earning its own interest partway through the year - so you actually end up with a bit more than 5%. APY (annual percentage yield) is that real yearly return, after compounding is included.

That is why APY is the fairer number to compare savings accounts: an account that compounds daily beats one that compounds yearly at the same advertised rate. The bar under the calculator shows a deposit (blue) and the interest one year of APY would add (green).

APY Formula

$$\text{APY} = \left(1 + \frac{r}{n}\right)^n - 1$$

Here r is the nominal annual rate written as a decimal and n is the number of compounding periods per year. For continuous compounding:

$$\text{APY} = e^r - 1$$

How to Use It

1. Enter the nominal interest rate (the stated yearly rate, before compounding).
2. Choose how often interest compounds (monthly, daily, and so on).
3. Optionally enter a deposit amount to see roughly what it earns in a year.

Worked Examples

Nominal rate	Compounding	APY
5%	Annually	5%
5%	Monthly	5.12%
5%	Daily	5.13%
6%	Quarterly	6.14%
10%	Monthly	10.47%

Common Uses

• Comparing savings accounts or CDs quoted with different compounding.
• Seeing the true yearly return behind a nominal rate.
• Checking how much more frequent compounding actually adds.

FAQ

What is APY?

APY (annual percentage yield) is the real yearly return once compounding is included. It shows how much you actually earn in a year, unlike the nominal rate, which ignores how often interest is added.

What is the difference between APY and the nominal rate (or APR)?

The nominal rate is the stated yearly rate before compounding. APY folds the compounding in, so for the same nominal rate, more frequent compounding produces a higher APY.

How is APY calculated?

Use $\text{APY} = \left(1 + \frac{r}{n}\right)^n - 1$, where r is the nominal annual rate as a decimal and n is the number of compounding periods per year. For continuous compounding, $\text{APY} = e^r - 1$.

Does more frequent compounding always give a higher APY?

Yes, for the same nominal rate. Daily beats monthly beats annually, but each step adds less, approaching the continuous-compounding limit.