Find the future value of an annuity of $1100 paid at the end of each year for 15 years, if interest is earned at a rate of 8%, compounded annually. (Round your answer to the nearest cent.)
$ 

To find the future value of an annuity where payments are made at the end of each period, we use the future value of an ordinary annuity formula:

\[
FV = P \times \frac{(1 + r)^n - 1}{r}
\]

where:
- $ P = 1100 $: the annual payment,
- $ r = 0.08 $: the annual interest rate,
- $ n = 15 $: the number of payments.

### Step-by-Step Calculation

1. **Calculate $(1 + r)^n$:**
   \[
   (1 + 0.08)^{15} = 3.1722
   \]

2. **Subtract 1 from the result:**
   \[
   3.1722 - 1 = 2.1722
   \]

3. **Divide by the interest rate $r$:**
   \[
   \frac{2.1722}{0.08} = 27.1525
   \]

4. **Multiply by the payment amount $P$:**
   \[
   1100 \times 27.1525 = 29867.75
   \]

### Final Answer
The future value of the annuity is approximately **$29,867.75**.

Would you like more details, or have any questions? 

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Here are five related questions to deepen your understanding:

1. How would the future value change if payments were made at the beginning of each period?
2. How does the interest rate affect the future value of an annuity?
3. What would the future value be if the payments were made semiannually instead of annually?
4. How does the number of years impact the future value in annuities with compound interest?
5. What is the difference in future value between simple interest and compound interest in this context?

**Tip:** For annuities, the payment timing (end vs. beginning) affects the future value—payments at the beginning grow more due to additional compounding.

Find the future value of an annuity of $1100 paid at the end of each year for 15 years, if interest is earned at a rate of 8%, compounded annually. (Round your answer to the nearest cent.)

Learn to find the future value of an annuity with annual payments of $1100 over 15 years at an 8% interest rate, compounded annually. This solution includes the future value formula, step-by-step calculations, and insights into annuities and compound interest. Ideal for high school students in Grades 11-12.

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