An investor wants to save money to purchase real estate. She buys an annuity with yearly payments that earn 5% interest, compounded annually. Payments will be made at the end of each year. Find the total value of the annuity in 16 years if each yearly payment is $759.

To find the total value of the annuity after 16 years, we can use the future value of an ordinary annuity formula:

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

Where:
- $FV$ is the future value of the annuity.
- $P$ is the yearly payment.
- $r$ is the annual interest rate.
- $n$ is the total number of payments.

Given:
- $P = 759$ dollars (yearly payment),
- Annual interest rate $r = 5\%$ or 0.05,
- Number of years $n = 16$.

Substituting these values into the formula:

\[
FV = 759 \times \frac{(1 + 0.05)^{16} - 1}{0.05}
\]

Let's calculate the future value $FV$.The total value of the annuity after 16 years is approximately **$17,956.04**.

Do you have any questions or need more details?

Here are 5 related questions:
1. How would the future value change if the interest rate were 6% instead of 5%?
2. What is the impact of making payments semi-annually instead of annually?
3. How would the future value differ if the investor saved for 20 years instead of 16?
4. What happens to the future value if the payments were made at the beginning of each year?
5. How can the investor compare different annuity options to choose the best one?

**Tip:** The future value of an annuity increases significantly with the number of periods and the interest rate, so consider these factors when planning long-term investments.

Discover how to calculate the total value of an annuity with 5% interest compounded annually. Each year, $759 payments are made, totaling 16 years. Get the detailed formula and step-by-step solution. Ideal for investment planning.

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