Given an ordinary annuity with periodic payments of $500, an annual interest rate of 8% compounded annually and a term of 10 years, what is the future value of this annuity? a. $7,204.29 b. $7,243.28 c. $7,131.33 d. $9,204.29

To find the future value (FV) of an ordinary annuity, we can use the formula:

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

Where:
- $P$ is the periodic payment (\$500 in this case),
- $r$ is the periodic interest rate (annual interest rate of 8% or 0.08),
- $n$ is the total number of periods (10 years).

Now, let's calculate it step by step:

1. **Substitute the known values:**

\[
FV = 500 \times \left(\frac{(1 + 0.08)^{10} - 1}{0.08}\right)
\]

2. **Calculate $(1 + 0.08)^{10}$:**

\[
(1 + 0.08)^{10} = 2.158924997
\]

3. **Subtract 1:**

\[
2.158924997 - 1 = 1.158924997
\]

4. **Divide by the interest rate (0.08):**

\[
\frac{1.158924997}{0.08} = 14.48656246
\]

5. **Multiply by the periodic payment (\$500):**

\[
FV = 500 \times 14.48656246 = 7,243.28
\]

Thus, the future value of the annuity is **\$7,243.28**.

The correct answer is **b. \$7,243.28**.

Would you like further details on how I calculated any part of this?

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Here are 5 related questions to explore further:

1. How would the future value change if the payments were made at the beginning of each period (annuity due)?
2. What would be the future value if the interest were compounded quarterly instead of annually?
3. How would increasing the annual interest rate affect the future value?
4. What is the present value of the same annuity, given the same interest rate and term?
5. How does the future value of an ordinary annuity compare to that of a growing annuity?

**Tip**: For ordinary annuities, payments are made at the end of each period. This contrasts with annuity due, where payments are made at the beginning, resulting in a slightly higher future value for the same terms.

Explore how to compute the future value of an ordinary annuity with periodic payments of $500, an 8% annual interest rate, and a 10-year term. This step-by-step solution covers key financial concepts, including annuity formulas and compound interest calculations. Ideal for finance students and professionals.

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