A person places $$ \$ 29800 $$ in an investment account earning an annual rate of $$ 3.5 \% $$, compounded continuously. Using the formula $$ V=P e^{r t} $$, where V is the value of the account in $$ t $$ years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 7 years.

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We start with the formula for continuously compounded interest:

$$
V = P e^{r t}
$$

where  
$$ P = 29800 $$ is the principal,  
$$ r = 0.035 $$ is the annual interest rate (expressed as a decimal), and  
$$ t = 7 $$ years.

Substitute the values into the formula:

$$
V = 29800 \times e^{0.035 \times 7}
$$

First, compute the product in the exponent:

$$
0.035 \times 7 = 0.245
$$

So the formula becomes:

$$
V = 29800 \times e^{0.245}
$$

Using a calculator to evaluate $$ e^{0.245} $$, we get approximately:

$$
e^{0.245} \approx 1.27761
$$

Now, multiply this value by 29800:

$$
V \approx 29800 \times 1.27761 \approx 38072.89
$$

Thus, the amount of money in the account after 7 years, rounded to the nearest cent, is:

$$
\boxed{\$38072.89}
$$
After 7 years, the account will have approximately \$38,072.89.

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