If you deposit $500 each month into an IRA earning 4.7% interest, how much will you have in the account after 14 years? Round your answer to the nearest cent.

This is a problem involving compound interest with regular monthly contributions. The future value of a series of regular contributions to an account earning compound interest can be calculated using the formula for the future value of an ordinary annuity:

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

where:
- $ FV $ is the future value of the account.
- $ P $ is the monthly deposit.
- $ r $ is the monthly interest rate (annual interest rate divided by 12).
- $ n $ is the total number of deposits (months).

### Given:
- $ P = 500 $ (monthly deposit),
- Annual interest rate = 4.7% = 0.047 (decimal),
- $ r = \frac{0.047}{12} \approx 0.00391667 $ (monthly interest rate),
- Time = 14 years, so $ n = 14 \times 12 = 168 $ months.

Now, I will calculate the future value using this information.After 14 years of depositing $500 each month into an IRA earning 4.7% interest, you will have approximately **$118,525.09** in the account.

Would you like further details or have any questions about the calculation?

Here are 5 related questions to explore further:
1. What if the interest rate were higher, say 6%? How much would you have?
2. How would your balance change if you made quarterly instead of monthly deposits?
3. What happens if you increase the monthly deposit amount over time?
4. How much of the total balance comes from your contributions versus interest earned?
5. What would be the impact of delaying the start of contributions by 5 years?

**Tip:** Compounding frequency significantly affects the growth of your investment. The more frequently the interest compounds, the faster the growth!

Discover how to calculate the future value of depositing $500 monthly into an IRA with 4.7% interest over 14 years. Learn the key concepts of compound interest, annuities, and financial growth. Perfect for Grades 10-12.

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