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 find out how much you will have after 6 years with continuous compounding, we can use the formula for continuous compound interest:

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

Where:
- $ A $ is the amount of money accumulated after $ t $ years, including interest.
- $ P $ is the principal amount (the initial amount of money), which is $13,000.
- $ r $ is the annual interest rate (in decimal form), which is 7%, or 0.07.
- $ t $ is the time the money is invested for, which is 6 years.
- $ e $ is the base of the natural logarithm, approximately equal to 2.71828.

Now, let's calculate the amount:

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

I'll calculate that now.After 6 years, you will have approximately **$19,785.50** in the account.

Do you want more details or have any questions?

Here are some related questions you might find interesting:
1. What would the amount be if the interest rate was 5% instead of 7%?
2. How does continuous compounding compare to annual compounding?
3. What is the formula for compound interest when it's compounded annually?
4. How much would you need to invest to have $20,000 after 6 years at 7% interest compounded continuously?
5. How long would it take to double your investment at 7% interest compounded continuously?
6. What happens to the total amount if the investment period is increased to 10 years?
7. What is the difference between continuous and simple interest?
8. How does the compound interest formula change if interest is compounded quarterly?

**Tip:** The concept of continuous compounding comes from calculus, where interest is added to the principal at every possible instant. This results in the maximum possible amount of interest over a given time period.

Find out how much money you will have after 6 years by investing $13,000 at 7% interest compounded continuously. Get a detailed solution using the continuous compound interest formula. Round the answer to the nearest cent.

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