To solve this problem, we will use the formula for the future value of an annuity, since Margo is making monthly deposits into her IRA. The formula for the future value $FV$ of an annuity compounded monthly is:

$FV = P \times \frac{(1 + r)^n - 1}{r}$

Where:

• $P$ is the monthly deposit (in dollars)
• $r$ is the monthly interest rate (annual interest rate divided by 12)
• $n$ is the total number of periods (number of months)

Given values:

• $P = 250$ (the monthly deposit)
• Annual interest rate $= 4.5\% = 0.045$
• Monthly interest rate $r = \frac{0.045}{12} = 0.00375$
• Time $t = 20$ years, so the total number of months is $n = 20 \times 12 = 240$

Now, substitute the values into the formula:

$FV = 250 \times \frac{(1 + 0.00375)^{240} - 1}{0.00375}$

Let’s calculate this step by step.

1. $1 + 0.00375 = 1.00375$
2. $1.00375^{240}$ (use a calculator for exponentiation): $1.00375^{240} \approx 2.454$
3. Subtract 1 from this value: $2.454 - 1 = 1.454$
4. Now, divide by the monthly interest rate: $\frac{1.454}{0.00375} \approx 387.7333$
5. Finally, multiply by the monthly deposit: $FV = 250 \times 387.7333 \approx 96933.33$

Conclusion:

The value of Margo's account after 20 years will be approximately $96,933.33.

Would you like more details on this process, or have any questions?

Here are some related questions for further exploration:

1. How would the value of the account change if Margo increased her monthly deposit to $300?
2. How would the account value change if the interest rate were increased to 5%?
3. What is the formula for the present value of an annuity, and how does it differ from the future value formula?
4. If Margo decided to withdraw money from her IRA each month instead of depositing, how would that affect the future value?
5. How would the account value change if Margo made deposits only once a year instead of monthly?

Tip: Small changes in the interest rate or the monthly deposit can make a big difference in the long-term value of an investment due to the power of compound interest.