Mental maths and numerical fluency

Small-return approximation

Converts between simple and continuously compounded returns in your head.

ln⁡(1+x)≈x−x22\ln(1+x) \approx x - \frac{x^2}{2}

Where

xx
The simple return, as a decimal.

Assumptions

  • Within a thousandth for ∣x∣|x| below about 0.05; it degrades quickly beyond that.

Sanity check. A 3% simple return is about 2.96% continuously compounded — always slightly smaller.

Where this is taught