https://file.aiquickdraw.com/mathbot/file/1727585449499ou22hvly.jpg

The problem in the image can be solved using the formula for the future value of an annuity with compound interest:

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

Where:
- $A$ is the future value of the investment.
- $P$ is the regular deposit amount ($450).
- $r$ is the annual interest rate (5% or 0.05).
- $n$ is the number of times the interest is compounded per year (monthly compounding, so $n = 12$).
- $t$ is the number of years the money is invested (from age 30 to 65, so $t = 35$).

Let's calculate how much Taylor will have saved by age 65.

### Step-by-step Calculation:

1. $ P = 450 $
2. $ r = 0.05 $
3. $ n = 12 $
4. $ t = 35 $

Substitute these values into the formula to compute the future value.

I'll do the calculation now.Taylor will have saved approximately **$511,241.59** by the time she retires at age 65.

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

Here are some related questions you might find useful:
1. What if Taylor deposits a different amount each month?
2. How much would Taylor save if the interest were compounded quarterly instead of monthly?
3. What if Taylor starts saving at age 25 instead of 30?
4. How would changes in the interest rate affect the final savings?
5. How much does Taylor's total contribution compare to the interest earned?

**Tip**: Starting retirement savings earlier allows compound interest more time to grow your investment exponentially.

Taylor starts an IRA (Individual Retirement Account) at the age of 30 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.

Learn how to calculate retirement savings using monthly deposits of $450 into an IRA, compounded monthly at 5% interest. This problem illustrates the power of compound interest and helps determine the total amount saved by the age of 65.

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