Find the future value of an annuity of 500 made annually for 7 years at interest rate of 14% compounded annually. Given that (1.14)=2.5023.

To find the future value of an annuity, we can use the Future Value of an Annuity (FVA) formula:

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

Where:
- $ P $ is the payment made each period (\$500 in this case).
- $ r $ is the interest rate per period (14% or 0.14).
- $ n $ is the number of periods (7 years).

Given:
- $ P = 500 $
- $ r = 0.14 $
- $ n = 7 $
- $ (1.14)^7 = 2.5023 $

Substituting the values into the formula:

\[
\text{FVA} = 500 \times \frac{2.5023 - 1}{0.14}
\]

Now, let's calculate this:

\[
\text{FVA} = 500 \times \frac{1.5023}{0.14} = 500 \times 10.7307 = 5365.35
\]

The future value of the annuity is **\$5,365.35**.

Would you like more details or have any questions?

Here are some related questions you might find interesting:

1. What would the future value be if the interest rate was 10% instead of 14%?
2. How does the future value change if the annuity is compounded semi-annually instead of annually?
3. What is the present value of the annuity given the same conditions?
4. How would the future value change if the annuity was paid monthly instead of annually?
5. What if the annuity was extended to 10 years with the same interest rate?

**Tip:** When working with annuities, always double-check whether the interest rate is compounded annually, semi-annually, or monthly, as it significantly impacts the calculations.

Learn how to calculate the future value of an annuity with $500 payments made annually over 7 years at a 14% interest rate. Detailed step-by-step solution provided using the Future Value of an Annuity (FVA) formula. Suitable for advanced high school students and finance enthusiasts.

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