APY Formula (Annual Percentage Yield)
The APY formula calculates the real rate of return on savings, accounting for compound interest frequency.
The Formula
APY = (1 + r/n)^n - 1
Variables
| Symbol | Meaning |
|---|---|
| APY | Annual Percentage Yield (actual yearly return) |
| r | Nominal annual interest rate (as a decimal) |
| n | Number of compounding periods per year |
Compounding Frequencies
| Frequency | n | APY at 5% rate |
|---|---|---|
| Annually | 1 | 5.000% |
| Semi-annually | 2 | 5.063% |
| Quarterly | 4 | 5.095% |
| Monthly | 12 | 5.116% |
| Daily | 365 | 5.127% |
| Continuously | ∞ | 5.127% (e^r - 1) |
APY vs APR
- APY — what you earn on savings and investments
- APR — what you pay on loans and credit cards
- Higher APY = better for savings
- Lower APR = better for borrowing
Example
A savings account pays 5% interest, compounded monthly. What is the APY?
APY = (1 + 0.05/12)^12 - 1
APY = (1.004167)^12 - 1
APY = 1.05116 - 1 = 5.116%
The actual yield is 5.116%, not 5%, thanks to monthly compounding.
On a $10,000 deposit, that is an extra $11.60 per year from compounding alone.