Bailey starts an IRA (Individual Retirement Account) at the age of 24 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.

To solve this problem, we can use the formula for the future value of an annuity, because Bailey is making regular monthly deposits into her IRA. The formula is:

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

Where:
- $FV$ is the future value of the annuity (how much money Bailey will have when she retires).
- $P$ is the monthly deposit ($450).
- $r$ is the monthly interest rate (the annual interest rate divided by 12).
- $n$ is the total number of monthly deposits (the number of months from age 24 to age 65).

### Step 1: Identify the values
- Monthly deposit: $P = 450$
- Annual interest rate: 5% → Monthly interest rate: $r = \frac{5\%}{12} = 0.004167$
- Bailey starts at age 24 and retires at age 65, so the number of years is $65 - 24 = 41$ years.
- The total number of months is $n = 41 \times 12 = 492$ months.

### Step 2: Plug the values into the formula

\[
FV = 450 \times \frac{(1 + 0.004167)^{492} - 1}{0.004167}
\]

Now, let's calculate the future value.

I'll compute this.It seems like I can’t do more advanced data analysis right now. Please try again later.

If you'd like, I can walk you through how to calculate this manually or suggest alternative ways to proceed!

Here are 5 related questions to expand your understanding:

1. How does compound interest differ from simple interest in retirement savings?
2. What would be the future value if the interest rate increased to 6%?
3. How does the frequency of compounding affect the amount saved in an IRA?
4. What if Bailey delayed her retirement by 5 more years? How would that impact her savings?
5. How would the total savings change if she started saving at age 30 instead of 24?

**Tip:** Starting retirement savings early helps the power of compound interest work longer, leading to significantly more savings.

Find out how much Bailey will have saved by the age of 65 in her IRA with monthly deposits of $450 and a 5% annual interest rate compounded monthly. Learn how to apply the future value of annuities formula to calculate long-term retirement savings.

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