You deposit $5,500 each year into an account earning 7% interest compounded annually.

How much will you have in the account in 11 years?

Do not round numbers while working on the problem.  Only round the final answer.

Since we are working with money, round to the cent.

To calculate the future value of an investment with regular annual deposits and compound interest, we use the **Future Value of an Annuity formula**:

\[
A = P \left( \frac{(1 + r)^n - 1}{r} \right)
\]

Where:
- $ A $ is the future value of the investment.
- $ P $ is the annual deposit ($5,500).
- $ r $ is the annual interest rate (7% or 0.07).
- $ n $ is the number of years the money is invested (11 years).

Plugging in the values:

\[
A = 5500 \left( \frac{(1 + 0.07)^{11} - 1}{0.07} \right)
\]

Let's first calculate the expression inside the formula.

\[
A = 5500 \left( \frac{(1.07)^{11} - 1}{0.07} \right)
\]

Now, let's determine the value of $ (1.07)^{11} $.

\[
1.07^{11} \approx 2.10533736
\]

Subtracting 1:

\[
2.10533736 - 1 = 1.10533736
\]

Next, divide by the interest rate (0.07):

\[
\frac{1.10533736}{0.07} \approx 15.7905337
\]

Finally, multiply by the annual deposit of $5,500:

\[
A = 5500 \times 15.7905337 \approx 86847.93535
\]

Rounded to the nearest cent (since we’re dealing with money):

\[
A \approx 86,847.94
\]

**Answer:** After 11 years, you will have approximately **$86,847.94** in the account.

---

Do you want more details or have any questions?

Here are 5 related questions you might find interesting:
1. What happens if the interest compounds monthly instead of annually?
2. How would the future value change if you deposited $7,500 each year instead?
3. What would be the total interest earned over the 11 years?
4. How does increasing the interest rate to 8% affect the final amount?
5. How much should you deposit annually to reach $100,000 in 11 years?

**Tip:** The key to calculating compound interest is understanding how the frequency of compounding (annually, monthly, etc.) impacts the growth of your investment over time.

Learn how to calculate the future value of an investment with annual deposits of $5,500 at 7% interest compounded annually over 11 years. This problem utilizes the Future Value of an Annuity formula and covers concepts like compound interest and exponential growth.

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