Bailey starts an IRA (Individual Retirement Account) at the age of 32
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 can be solved using the formula for the future value of an ordinary annuity, which accounts for regular payments and compounded interest. The formula is:

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

Where:
- $A$ is the future value of the annuity (the amount Bailey will have saved),
- $P$ 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 (monthly, so $n = 12$),
- $t$ is the number of years until retirement (from age 32 to 65, so $t = 65 - 32 = 33$).

Let's calculate the future value step by step.

\[
A = 450 \times \frac{(1 + \frac{0.05}{12})^{12 \times 33} - 1}{\frac{0.05}{12}}
\]

I'll compute this now.Bailey will have saved approximately **$452,429.38** by the time she retires at the age of 65.

Would you like more details on the calculation, or do you have any questions?

Here are 5 related questions to further explore the topic:
1. What if the interest rate was 6% instead of 5%?
2. How much more would Bailey save if she deposited $500 per month?
3. What if Bailey started saving at age 25 instead of 32?
4. How would the total amount change if the interest was compounded quarterly instead of monthly?
5. What if Bailey withdrew $100,000 at age 55 and then continued her monthly deposits?

**Tip:** Starting to save earlier or increasing your monthly contribution can significantly increase retirement savings due to compound interest.

Bailey starts an IRA (Individual Retirement Account) at the age of 32 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.

Calculate how much Bailey will save by retirement using monthly deposits of $450 into an IRA with 5% interest compounded monthly. This problem explores the future value of an annuity and compound interest concepts. Suitable for students in Grades 10-12.

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