The Natural Base e

We want to find the amount in a continuously compounded account for the given conditions. $$\begin{array}{rl}\text{Principal:}& \$2000\\ \text{Annual interest rate:}& 5.1\%\\ \text{Time:}& 3\text{ years}\end{array}$$ To do so, we will start by recalling the formula for continuously compounded interest. $$\begin{array}{c}A(t)=P\cdot e^{rt}\end{array}$$ In this formula, $A(t)$ represents the amount in the account at time $t,$ $P$ represents the initial value of the account or the principal, $r$ is the annual interest rate, and $t$ is the time in years. Let's substitute the given values into the formula. Note that $r$ should be expressed as a decimal, so $5.1\%=0.051.$ The amount after $3$ years under the given conditions is approximately $\$2330.65.$