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The formula used to calculate the future value of an ordinary annuity, where periodic payments are made at the end of each period, is:

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

Where:
- $FV$ = Future Value of the annuity
- $P$ = Payment amount per period
- $r$ = Periodic interest rate (annual interest rate divided by the number of compounding periods per year)
- $n$ = Total number of payments (number of periods per year multiplied by the number of years)

Let's break this down for your specific case:

- Monthly payments ($P$) = \$591
- Annual interest rate = 5.14% compounded monthly, so $r = \frac{5.14\%}{12} = \frac{0.0514}{12}$
- For 3 years, $n = 3 \times 12 = 36$ periods
- For 9 years, $n = 9 \times 12 = 108$ periods

Now, I'll calculate both the 3-year and 9-year future values using this formula.The future values of the annuity are as follows:

- After 3 years, the amount in the account will be approximately **\$22,951.05**.
- After 9 years, the amount in the account will be approximately **\$80,941.20**.

Would you like any additional details or have any questions?

Here are some related questions you might find interesting:
1. What is the total interest earned in the account after 3 and 9 years?
2. How would changing the interest rate affect the future values?
3. How much would you need to deposit monthly to reach \$100,000 in 9 years?
4. What if the payments were made at the beginning of each period (annuity due)?
5. How would increasing the payment amount to \$700/month change the outcome?

**Tip:** To better plan your savings, experiment with different time frames or payment amounts to see how much you can accumulate based on your goals.

If you make monthly payments of $591.00 into an ordinary annuity earning an annual interest rate of 5.14% compounded monthly, how much will you have in the account after 3 years? After 9 years?

Learn how to calculate the future value of an ordinary annuity with monthly payments of $591.00 and an annual interest rate of 5.14% compounded monthly. Discover the accumulated amount after 3 years ($22,951.05) and after 9 years ($80,941.20). This problem involves key finance concepts such as annuities, compound interest, and time value of money.

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