Calculating Continuous Growth

A person invested $1,000 in an account earning a nominal 10% per year compounded continuously. How much was in the account at the end of one year?

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
Since the account is growing in value, this is a continuous compounding problem with growth rate $r = 0.10.$ The initial investment was $1,000, so $P = 1000.$ We use the continuous compounding formula to find the value after $t = 1$ year:

$\begin{array}{l} A (t) & = P e^{r t} & Use the continuous compounding formula . \\ = 1000 {(e)}^{0.1} \begin{matrix} \end{matrix} & Substitute known values for P, r, and t . \\ \approx 1105.17 & Use a calculator to approximate . \end{array}$
The account is worth $1,105.17 after one year.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

A person invests $100,000 at a nominal 12% interest per year compounded continuously. What will be the value of the investment in 30 years?

How did it go?