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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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$The value of her investment after 6 years will be approximately $11597.06$

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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 $A = P e^{r t}$ , 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 ： $The value of her investment after 6 years will be approximately $11597.06$

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