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The problem asks to calculate the future value of an investment with continuous compounding. The formula for continuous compound interest is:

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

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

Given:
- $ P = 2400 $ (the initial deposit),
- $ r = 5.5\% = 0.055 $ (the annual interest rate),
- $ t = 7 $ years.

Let's calculate the final amount $ A $.

\[
A = 2400 \times e^{0.055 \times 7}
\]

Now, I'll compute the value.

\[
A = 2400 \times e^{0.385}
\]

Approximating $ e^{0.385} $:

\[
e^{0.385} \approx 1.46984
\]

Therefore,

\[
A = 2400 \times 1.46984 \approx 3527.62
\]

So, Keisha will have approximately **$3,527.62** after 7 years.

Would you like more details on this, or do you have any questions?

Here are 5 questions to expand on this topic:
1. What would happen to the final amount if the interest rate increased to 6%?
2. How does continuous compounding differ from annual compounding?
3. Can you calculate how long it would take for Keisha's deposit to double at the same interest rate?
4. What would the final amount be if she deposited $3,000 instead?
5. How would the result change if the interest were compounded annually instead of continuously?

**Tip:** Continuous compounding grows money faster than discrete compounding because the interest is constantly calculated and added back into the principal.

Moneysaver's Bank offers a savings account that earns 5.5% interest per year, compounded continuously. If Keisha deposits $2400, how much will she have in the account after seven years, assuming she makes no withdrawals?

Calculate the future value of a $2400 deposit in a savings account with 5.5% continuous compounding interest over 7 years. Understand the continuous compounding formula and exponential growth. Suitable for high school students in Grades 9-12.

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