Question 21 of 30 , Step 1 of 1
$2 \theta / 33$
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10
Melanie invests $\$ 8800$ in a new savings account which earns $4.6 \%$ annual interest, compounded continuously, What will be the value of her investment after 6 years? Round to the nearest cent.
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\(\boxed{\text{The value of her investment after 6 years will be approximately \$11597.06}}\)
Step 1 ：Let the principal amount \(P = \$8800\), the annual interest rate \(r = 4.6\% = 0.046\), and the time \(t = 6\) years.
Step 2 ：The formula for continuous compound interest is \(A = P e^{rt}\), where \(A\) is the amount of money accumulated after n years, including interest.
Step 3 ：Substitute \(P = \$8800\), \(r = 0.046\), and \(t = 6\) into the formula: \(A = 8800 \cdot e^{0.046 \cdot 6}\).
Step 4 ：Calculate the value of \(A\): \(A \approx \$11597.06\).
Step 5 ：\(\boxed{\text{The value of her investment after 6 years will be approximately \$11597.06}}\)
