suppose you invest 10,000 in an account earning interest at a 2% annual rate compounded continuously how much money is in the account after 5 years round to 2 decimal places

To calculate the amount of money in the account after 5 years with continuous compounding, we use the formula:

\[
A = P e^{rt}
\]

where:
- $ A $ is the final amount in the account,
- $ P $ is the principal (initial investment),
- $ r $ is the annual interest rate (expressed as a decimal),
- $ t $ is the time in years,
- $ e $ is the base of the natural logarithm (approximately 2.71828).

Given:
- $ P = 10,000 $,
- $ r = 0.02 $ (2% annual interest rate),
- $ t = 5 $ years.

Let's calculate:

\[
A = 10,000 \cdot e^{(0.02 \cdot 5)}
\]

I’ll compute the final value for you.After 5 years, with an initial investment of $10,000 at a 2% annual interest rate compounded continuously, the amount in the account will be **$11,051.71**.

Would you like further explanation or details on the calculation?

Here are 5 related questions to expand on this:
1. How does continuous compounding differ from monthly or annual compounding?
2. What would the final amount be if the interest rate was 3% instead of 2%?
3. How does the final amount change with different compounding periods (monthly, quarterly)?
4. How long would it take for the investment to double at a 2% continuous interest rate?
5. What is the difference between simple interest and compound interest?

**Tip**: Continuous compounding grows money faster than periodic compounding because it calculates interest an infinite number of times per year.

Suppose you invest 10,000 in an account earning interest at a 2% annual rate compounded continuously. How much money is in the account after 5 years? Round to 2 decimal places.

Learn how to calculate the future value of an investment using the continuous compound interest formula. In this problem, we compute the amount after investing $10,000 at a 2% annual interest rate compounded continuously for 5 years, resulting in $11,051.71. Perfect for high school students exploring exponential growth and finance.

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