Bailey starts an IRA (Individual Retirement Account) at the age of 30
to save for retirement. She deposits $350
each month. The IRA has an average annual interest rate of 6%
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 a series of regular payments (an ordinary annuity) with compound interest. The formula is:

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

Where:
- $A$ is the amount of money saved in the account after the given time.
- $P$ is the regular payment (in this case, $350).
- $r$ is the annual interest rate (6%, or 0.06 as a decimal).
- $n$ is the number of times the interest is compounded per year (monthly means $n = 12$).
- $t$ is the time in years (from age 30 to 65, meaning $t = 35$ years).

Now, we can substitute the values into the formula and solve for $A$.

\[
A = 350 \times \frac{(1 + 0.06/12)^{12 \times 35} - 1}{0.06/12}
\]

Let me calculate this.Bailey will have saved approximately **$498,648.60** by the time she retires at the age of 65.

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

Here are five related questions to explore:
1. What if Bailey started saving at age 25 instead of 30?
2. How much would Bailey save if the interest rate was 5% instead of 6%?
3. What if Bailey could only deposit $200 monthly instead of $350?
4. How much interest will Bailey have earned by the time she retires?
5. How does the amount change if the interest is compounded quarterly instead of monthly?

**Tip:** Starting early with compound interest significantly increases savings over time due to the power of exponential growth.

Bailey starts an IRA (Individual Retirement Account) at the age of 30 to save for retirement. She deposits $350 each month. The IRA has an average annual interest rate of 6% 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.

Learn how to calculate the future value of an IRA with monthly contributions of $350 and a 6% interest rate compounded monthly. By retirement at age 65, Bailey will have saved approximately $498,648.60. Explore related scenarios such as changing the contribution amount, interest rate, or compounding frequency.

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