Kadeem deposits $860 every year into an account earning an annual interest rate of 8.9% compounded annually. How much would he have in the account after 14 years, to the nearest dollar?

To find out how much Kadeem would have in his account after 14 years with annual deposits and compound interest, we use the formula for the future value of an annuity compounded annually:

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

where:
- $ A $ is the amount in the account after $ n $ years.
- $ P $ is the annual deposit ($860).
- $ r $ is the annual interest rate (8.9% or 0.089).
- $ n $ is the number of years (14).

Plugging in the values:

\[ A = 860 \left( \frac{(1 + 0.089)^{14} - 1}{0.089} \right) \]

First, calculate $ (1 + 0.089)^{14} $:

\[ (1.089)^{14} \approx 3.3373 \]

Then, calculate the future value of the annuity:

\[ A = 860 \left( \frac{3.3373 - 1}{0.089} \right) \]
\[ A = 860 \left( \frac{2.3373}{0.089} \right) \]
\[ A = 860 \times 26.2618 \]
\[ A \approx 22,583.15 \]

Therefore, Kadeem would have approximately $22,583 in the account after 14 years.

Would you like more details or have any questions? Here are some questions you might find interesting:

1. How does the compound interest formula work for different compounding periods?
2. What if Kadeem changes the amount he deposits each year?
3. How would the final amount change if the interest rate was different?
4. How does the future value formula change if interest is compounded monthly instead of annually?
5. What is the difference between simple interest and compound interest?

**Tip:** When solving compound interest problems, carefully check if the interest rate and compounding frequency are aligned, and always convert percentages to decimals in calculations.

Discover how to calculate the future value of an annuity with annual deposits, using compound interest. This problem involves annual deposits, an annual interest rate of 8.9%, and a 14-year period. Suitable for advanced high school students and those studying financial mathematics.

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