Gabe opened a savings account and deposited $3,000.00 as principal. The account earns 13% interest, compounded continuously. What is the balance after 9 years?


To find the balance of an account with continuously compounded interest, we use the formula:

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

Where:
- $ A $ is the amount of money after time $ t $ (the balance),
- $ P $ is the principal amount (initial deposit),
- $ r $ is the annual interest rate (as a decimal),
- $ t $ is the time in years,
- $ e $ is Euler's number (approximately 2.71828).

### Given:
- $ P = 3000 $,
- $ r = 0.13 $ (since 13% = 0.13),
- $ t = 9 $.

Now, we can substitute these values into the formula:

\[
A = 3000 \times e^{0.13 \times 9}
\]

Let me calculate that for you.The balance of Gabe's account after 9 years, with 13% interest compounded continuously, will be approximately **$9,665.98**.

Would you like more details or have any questions? Here are 5 related questions to explore further:

1. How would the balance change if the interest rate were 10% instead of 13%?
2. What would be the balance if the interest were compounded annually instead of continuously?
3. How does the balance change if Gabe deposits $5,000 instead of $3,000?
4. What is the formula for continuously compounded interest, and how is it derived?
5. What would be the future value if the time period were extended to 15 years?

**Tip:** Continuously compounded interest grows faster than any other compounding frequency (e.g., monthly, quarterly, or annually).

Gabe opened a savings account and deposited $3,000.00 as principal. The account earns 13% interest, compounded continuously. What is the balance after 9 years?

Learn how to calculate the balance of a savings account with $3,000 principal and 13% interest compounded continuously over 9 years. This problem involves exponential growth and the continuous compound interest formula. Suitable for students in Grades 10-12.

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