Margo starts an individual retirement account (IRA) by depositing $350 at the beginning of each month into an account that earns 4.5% interest compounded monthly. If she continues this plan for 20 years, what will be the value (in dollars) of her account?

To calculate the value of Margo's IRA account after 20 years, we will use the **future value of an annuity formula**, since she is making regular monthly deposits into an account that earns interest.

The formula for the future value of an annuity compounded monthly is:

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

Where:
- $A$ = future value of the account
- $P$ = monthly deposit (\$350)
- $r$ = annual interest rate (4.5% = 0.045)
- $n$ = number of times the interest is compounded per year (monthly = 12)
- $t$ = number of years (20 years)

Now, let's plug in the values:
- $P = 350$
- $r = 0.045$
- $n = 12$
- $t = 20$

I'll calculate this step-by-step to find the future value.The value of Margo's IRA account after 20 years will be approximately **$136,352.94**.

Would you like further details on how this calculation was made, or do you have any other questions?

Here are 5 related questions to expand on this concept:
1. What would happen if Margo made larger monthly contributions?
2. How does the interest rate affect the future value of an annuity?
3. What if the interest was compounded quarterly instead of monthly?
4. How would the value change if Margo contributed for 25 years instead of 20?
5. How does the future value change if the contributions are made at the end of each month instead?

**Tip**: Compounding interest significantly increases the future value over long periods, especially when contributions are regular.

Margo starts an individual retirement account (IRA) by depositing $350 at the beginning of each month into an account that earns 4.5% interest compounded monthly. If she continues this plan for 20 years, what will be the value (in dollars) of her account?

Discover how to calculate the future value of an IRA with $350 monthly contributions at 4.5% interest compounded monthly over 20 years. This problem involves concepts like future value of annuities and compound interest, offering a step-by-step breakdown suitable for high school students.

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