Binomial Approximation

The first-order binomial approximation, $(1+x)^n \approx 1+xn$, is useful for estimation problems where $|xn|$ is much less than 1. These problems often multiply the result by a large integer to provide a sufficient range for the answer.

For example, $1000(1.0002)^{50} \approx 1000[1 + (0.0002 \times 50)] = 1000(1.01) = 1010$.