Question 6 of 15, Step 1 of 1 \( 4 / 15 \) 1 Correct Incorrect Suppose an investment earns \( 2.2 \% \) interest compounded continuously. Find the future value of a \( \$ 2100 \) investment after 13 years. Round your answer to the nearest cent, If necessary. Formulas Simple Interest \[ \begin{array}{l} I=P r t \\ A=P(1+r t) \\ A=P\left(1+\frac{r}{n}\right)^{n t} \end{array} \] Future Value for Simple Interest Future Value for Compound Interest Future Value for Continuous Compound Interest \[ \begin{array}{l} A=P e^{n t} \\ A P Y=\left(1+\frac{r}{n}\right)^{n}-1 \end{array} \] Annual Percentage Yield (APY) Answer Keypad Keybo ird Shortcutrar

To calculate the future value of an investment using continuous compounding, we use the formula \( A = P e^{rt} \). In this case, \( P = 2100 \), \( r = 0.022 \) (2.2%), and \( t = 13 \) years. Plugging in the numbers gives you the future value, which becomes \( A = 2100 e^{0.022 \times 13} \). After crunching the numbers, you'll find that the future value is approximately \( \$2,969.72 \). Continuous compounding may sound like rocket science, but the basic concept is that your investment grows faster than traditional compounding! This is because you earn interest not just on your principal but also on the growing interest, continuously over the time period. It's like a money-making snowball that gathers pace as it rolls downhill, putting your bucks to work 24/7!