Banking
Continuous compounding limit
The upper bound as compounding frequency approaches infinity. On a 5% nominal rate this is 5.12711% — only marginally above daily compounding.
The Formula
APY = e^r - 1
The upper bound as compounding frequency approaches infinity. On a 5% nominal rate this is 5.12711% — only marginally above daily compounding.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| e | Euler's number | constant | Approximately 2.71828. Use exp(r) - 1 rather than typing the constant. |
What Each Symbol Means
econstant
Euler's number
Approximately 2.71828. Use exp(r) - 1 rather than typing the constant.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate apy page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate APY, filed under Finance. Every number the guide produces comes from substituting into this one line.