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The question you provided can be solved using the formula for the future value of an annuity since Bailey is making monthly deposits. The formula for the future value of an annuity compounded monthly is:

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

Where:
- $ FV $ is the future value of the account.
- $ P $ is the monthly deposit ($450).
- $ r $ is the annual interest rate (5% or 0.05).
- $ n $ is the number of times the interest is compounded per year (12 for monthly compounding).
- $ t $ is the number of years the money is invested (65 - 34 = 31 years).

Let’s calculate the future value of Bailey’s retirement account.

I'll proceed with this calculation now.The future value of Bailey's retirement account when she retires at the age of 65 will be approximately **$399,202.84**.

Would you like more details or have any questions about this calculation?

Here are 5 related questions to explore:
1. How would the final amount change if Bailey deposited $500 each month instead of $450?
2. What if the interest rate were 6% instead of 5%? How would that affect her savings?
3. How would the future value be affected if Bailey started saving at age 30 instead of 34?
4. What if the interest was compounded quarterly instead of monthly?
5. How much of the total amount will be from Bailey's contributions, and how much will come from interest?

**Tip:** Increasing the frequency of compounding (e.g., monthly vs. annually) slightly increases the final amount due to interest compounding on a more regular basis.

Bailey starts an IRA (Individual Retirement Account) at the age of 34 to save for retirement. She deposits $450 each month. The IRA has an average annual interest rate of 5% compounded monthly. How much money will she have saved when she retires at the age of 65? Round your answer to the nearest cent, if necessary.

This problem involves calculating the future value of Bailey's retirement savings. Bailey deposits $450 monthly into an IRA with a 5% interest rate compounded monthly for 31 years. Learn how to solve this using the future value of an annuity formula. Suitable for high school and college-level students.

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