A person places $$ \$ 48800 $$ in an investment account earning an annual rate of $$ 3.1 \% $$, compounded continuously. Using the formula $$ V=P e^{r t} $$, where $$ V $$ is the value of the account in tyears, $$ P $$ 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 13 years.

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Given:
- Initial investment, $$ P = \$48800 $$
- Annual rate of interest, $$ r = 3.1\% = 0.031 $$
- Time, $$ t = 13 $$ years

The formula to calculate the value of the account after $$ t $$ years is:
$$ V = P e^{rt} $$

Substitute the given values into the formula:
$$ V = 48800 e^{0.031 \times 13} $$

Now, we can calculate the value of the account after 13 years using the formula.
Calculate the value by following steps:
- step0: Calculate:
  $$48800e^{0.031\times 13}$$
- step1: Multiply the numbers:
  $$48800e^{0.403}$$
- step2: Convert the expressions:
  $$48800e^{\frac{403}{1000}}$$
- step3: Rewrite the expression:
  $$48800\sqrt[1000]{e^{403}}$$
The amount of money in the account after 13 years is approximately $73,019.78 to the nearest cent.
The amount of money in the account after 13 years is approximately \$73,019.78.

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