The timpanist for an orchestra deposits $250 at the beginning of each month in a Roth IRA. The IRA has an annual interest rate of 5.5% compounded monthly. Find the value of the Roth IRA (in dollars) after 12 years.

To calculate the future value of the Roth IRA after 12 years, we can use the future value of a series formula for compound interest:

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

Where:
- $ A $ = the future value of the investment/annuity.
- $ P $ = the amount of each monthly deposit ($250).
- $ r $ = annual interest rate (5.5% or 0.055).
- $ n $ = the number of times the interest is compounded per year (12 for monthly compounding).
- $ t $ = the number of years (12 years).

Let's plug in the values and compute this step by step.

\[
P = 250, \quad r = 0.055, \quad n = 12, \quad t = 12
\]

Now, I'll calculate the value of the Roth IRA after 12 years.The value of the Roth IRA after 12 years is approximately **$50,829.66**.

Do you want further details or have any questions? 

Here are 5 related questions to expand on this:
1. How would the value change if the interest rate was 6% instead of 5.5%?
2. What if the timpanist increased the monthly deposit to $300?
3. How does monthly compounding compare to annual compounding for this investment?
4. How long would it take for the Roth IRA to double with the same monthly contributions and interest rate?
5. What would the future value be if the investment period was 15 years instead of 12?

**Tip:** Even small increases in the interest rate or deposit amount can make a significant difference in long-term investments.

The timpanist for an orchestra deposits $250 at the beginning of each month in a Roth IRA. The IRA has an annual interest rate of 5.5% compounded monthly. Find the value of the Roth IRA (in dollars) after 12 years.

Find out how to calculate the future value of a Roth IRA with $250 monthly deposits, a 5.5% annual interest rate compounded monthly, over a 12-year period. This step-by-step guide uses the compound interest formula to determine the final value, suitable for students in Grades 10-12.

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