A person places $62700 in an investment account earning an annual rate of 2.6%, compounded continuously. Using the formula V, equals, P, e, start superscript, r, t, end superscript*V*=*Pe*$$ ^{rt} $$$$  $$, 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 18 years.

To find the amount of money in the account after 18 years using the formula for continuous compounding:

\[
V = P \cdot e^{rt}
\]

where:
- $ P = 62700 $ (the principal),
- $ r = 0.026 $ (the annual interest rate, 2.6% expressed as a decimal),
- $ t = 18 $ years,
- $ e $ is the base of the natural logarithm (approximately 2.71828).

Substitute the values into the formula:

\[
V = 62700 \cdot e^{0.026 \times 18}
\]

First, calculate the exponent:

\[
0.026 \times 18 = 0.468
\]

Next, calculate $ e^{0.468} $:

\[
e^{0.468} \approx 1.5978
\]

Finally, multiply by the principal:

\[
V = 62700 \times 1.5978 \approx 100100.06
\]

Therefore, the amount of money in the account after 18 years, to the nearest cent, is **$100,100.06**.

Would you like to explore further details or have any additional questions? Here are some related questions:

1. What would be the value after 10 years instead of 18 years?
2. How does the investment value change if the interest rate increases to 3%?
3. What happens to the final amount if the initial investment is doubled?
4. How would the final amount differ if compounded quarterly instead of continuously?
5. Can you calculate the time it would take for the investment to double at this interest rate?

**Tip:** Remember, continuous compounding is the most effective way to grow an investment because it accounts for interest being added at every moment.

Learn how to calculate the growth of an investment using continuous compounding. This problem involves determining the amount of money in an investment account after 18 years with a principal of $62,700, an annual interest rate of 2.6% compounded continuously.

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