Ling opened a savings account 7 years ago. The account earns 9% interest, compounded continuously. If the current balance is $2,000.00, how much did she deposit initially?
Round your answer to the nearest cent.

To determine how much Ling deposited initially, we can use the formula for continuous compounding:

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

Where:
- $ A $ is the current amount in the account (final amount),
- $ P $ is the initial deposit (the value we need to find),
- $ r $ is the interest rate (as a decimal),
- $ t $ is the time in years,
- $ e $ is Euler's number (approximately 2.71828).

### Given:
- $ A = 2000 $,
- $ r = 9\% = 0.09 $,
- $ t = 7 $ years.

Now, we rearrange the formula to solve for $ P $:

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

Substitute the known values:

\[
P = \frac{2000}{e^{0.09 \cdot 7}}
\]

Let's compute that.Ling initially deposited approximately \$1,065.18 in her savings account.

Would you like any additional details or explanations?

Here are 5 related questions to deepen your understanding:
1. What is the formula for compound interest (not continuous)?
2. How would the initial deposit change if the interest rate were 8% instead of 9%?
3. What if the interest were compounded yearly instead of continuously?
4. How would the balance change if she had deposited \$3,000 instead of \$2,000?
5. What is Euler's number, and why is it used in continuous compounding?

**Tip:** Continuous compounding means the interest is being added to the principal constantly, which results in the fastest growth compared to other compounding intervals.

Ling opened a savings account 7 years ago. The account earns 9% interest, compounded continuously. If the current balance is $2,000.00, how much did she deposit initially? Round your answer to the nearest cent.

Discover how to calculate the initial deposit in a savings account using the continuous compounding interest formula. Given an interest rate of 9% over 7 years and a final balance of $2,000, learn how to find the initial deposit using exponential functions. Suitable for students in Grades 10-12.

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