Molly starts an IRA (Individual Retirement Account) at the age of 24 to save for retirement. She deposits $400 each month. The IRA has an average annual interest rate of 7% 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 determine how much Molly will have saved when she retires at the age of 65, we need to calculate the future value of an ordinary annuity, where she deposits \$400 each month into an IRA with an annual interest rate of 7%, compounded monthly.

### Step 1: Identify Key Variables

Let's define the key variables needed for the calculation:

- **Monthly Deposit (P):** \$400
- **Annual Interest Rate (r):** 7%, or 0.07 as a decimal
- **Compounding Periods per Year (n):** 12 (monthly compounding)
- **Number of Years (t):** From age 24 to 65, which is:
  \[
  t = 65 - 24 = 41 \text{ years}
  \]
- **Total Number of Compounding Periods (N):**
  \[
  N = n \times t = 12 \times 41 = 492 \text{ months}
  \]
- **Monthly Interest Rate (i):** The interest rate per compounding period (monthly):
  \[
  i = \frac{r}{n} = \frac{0.07}{12} \approx 0.0058333
  \]

### Step 2: Use the Future Value of an Ordinary Annuity Formula

The future value $ FV $ of an ordinary annuity can be calculated using the formula:

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

Where:
- $ P = 400 $ (monthly deposit)
- $ i = 0.0058333 $ (monthly interest rate)
- $ N = 492 $ (total number of deposits)

### Step 3: Substitute the Values into the Formula

Now, let's calculate the future value:

\[
FV = 400 \times \frac{(1 + 0.0058333)^{492} - 1}{0.0058333}
\]

Let's compute this step-by-step to find the total savings amount.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, I can guide you on how to calculate this manually if you'd like:

1. **Compute the monthly interest rate**:  
   \[
   i = \frac{0.07}{12} \approx 0.0058333
   \]

2. **Calculate the total number of deposits**:  
   \[
   N = 12 \times 41 = 492
   \]

3. **Use the future value formula** for an ordinary annuity:  
   \[
   FV = 400 \times \frac{(1 + 0.0058333)^{492} - 1}{0.0058333}
   \]

You can use a calculator or spreadsheet to compute the exact value.

Would you like help with something else, or do you have any other questions? Here are some suggestions:

1. How much would Molly save if she deposited a different amount each month?
2. What would happen if the interest rate were lower or higher?
3. How would saving bi-monthly or quarterly impact the

Molly starts an IRA (Individual Retirement Account) at the age of 24 to save for retirement. She deposits $400 each month. The IRA has an average annual interest rate of 7% 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 Individual Retirement Account (IRA) with a monthly deposit of $400, a 7% annual interest rate compounded monthly, over a period of 41 years. This detailed solution demonstrates key mathematical concepts such as compound interest and the future value of an ordinary annuity. Suitable for high school students in Grades 10-12.

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