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