#### Explanation:

The formula for compound interest calculation where the compounding occurs continuously is:

${A}_{t} = P {e}^{r t}$

Where:

${A}_{t}$ is the amount after $t$ years
$P$ is the principal amount
$r$ is the annual interest rate
$e$ is Euler's number $\approx 2.71828$

In this example: P=$100, r=4.5% = 0.045 $\therefore {P}_{2} = 100 \times {e}^{0.045 \times 2}$$\approx 100 \times {2.71828}^{0.09}$=$109.42 To 2D

NB: For those interested in the derivation of the formula it stems from the limit definition of $e$. Also see: http://www.milefoot.com/math/calculus/limits/LimitDefinitionOfE10.htm