Question 18 of 24, Step 1 of 1
Correct
2
Suppose an investment earns $1.9 \%$ interest compounded continuously. Find the future value of a $\$ 2200$ investment after 13 years. Round your answer to the nearest cent, if necessary.
Answer
Keypad
Keyboard Shortcuts
Submit Answer
Answer
\(\boxed{\text{The future value of the investment after 13 years is approximately \$2816.39.}}\)
Step 1 ：Let's denote the principal amount as \(P = \$2200\), the annual interest rate as \(r = 1.9\% = 0.019\), and the time in years as \(t = 13\) years.
Step 2 ：The formula for the future value \(A\) of an investment compounded continuously is given by \(A = P \cdot e^{rt}\).
Step 3 ：Substitute \(P = \$2200\), \(r = 0.019\), and \(t = 13\) years into the formula, we get \(A = 2200 \cdot e^{0.019 \cdot 13}\).
Step 4 ：Calculate the future value \(A\), we get \(A \approx \$2816.39\).
Step 5 ：\(\boxed{\text{The future value of the investment after 13 years is approximately \$2816.39.}}\)
