suppose you invest $13000 in an account that earns 7% interest compounded continuously. How much will you have after 6 years? Round the answer to the nearest cent.

To solve this problem, we can use the formula for continuously compounded interest, which is:

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

Where:
- $ A $ is the amount of money accumulated after $ t $ years, including interest.
- $ P $ is the principal amount (the initial amount of money).
- $ r $ is the annual interest rate (as a decimal).
- $ t $ is the time the money is invested for, in years.
- $ e $ is the base of the natural logarithm, approximately equal to 2.71828.

Given:
- $ P = 13000 $ dollars
- $ r = 7\% = 0.07 $
- $ t = 6 $ years

Substitute these values into the formula:

\[
A = 13000 \cdot e^{0.07 \times 6}
\]

Now, calculate the exponent:

\[
A = 13000 \cdot e^{0.42}
\]

Let's calculate $ e^{0.42} $ and then multiply by 13000.After 6 years, the amount in the account will be **$19,785.50** when rounded to the nearest cent.

Would you like more details or have any questions? 

Here are 8 related questions you might find interesting:
1. How does the calculation change if the interest rate increases to 8%?
2. What would be the total amount after 10 years instead of 6?
3. How does continuous compounding compare to monthly compounding?
4. What is the formula for compound interest if it’s not compounded continuously?
5. How much interest is earned after 6 years?
6. How does the principal amount affect the final accumulated value?
7. What happens if you withdraw some money after 3 years? How do you recalculate the interest?
8. How does the time period influence the total amount?

**Tip:** Continuously compounded interest grows faster than interest compounded periodically because the interest is being added to the principal at every moment.

Learn how to calculate the amount after 6 years of continuously compounded interest on a $13000 principal at a 7% interest rate. Understand the formula for continuous compounding and see step-by-step calculation. Round the answer to the nearest cent.

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