If you deposit $150 each month into a Roth IRA earning 6% annual interest compounded monthly, how much will you have in the account after 30 years? (Round your answer to the nearest cent.)

This is a compound interest problem involving regular monthly deposits into an account. The formula to calculate the future value of such an investment with regular contributions is:

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

Where:
- $ A $ is the future value of the investment.
- $ P $ is the monthly deposit ($150).
- $ r $ is the annual interest rate (6% or 0.06).
- $ n $ is the number of times the interest is compounded per year (monthly compounding means $ n = 12 $).
- $ t $ is the number of years (30 years).

Now, let's compute:

1. Monthly interest rate: $ \frac{r}{n} = \frac{0.06}{12} = 0.005 $
2. Total number of months: $ n \times t = 12 \times 30 = 360 $

Substitute these values into the formula:

\[
A = 150 \times \frac{(1 + 0.005)^{360} - 1}{0.005}
\]

I will now calculate this.After 30 years, the Roth IRA account will have approximately **$150,677.26** if you deposit $150 each month at an annual interest rate of 6% compounded monthly.

Would you like further details or have any questions? Here are some related questions to explore:

1. What if you increase the monthly contribution to $200?
2. How does the total amount change with a 7% interest rate instead of 6%?
3. How much interest would you earn in total after 30 years?
4. What would the balance be after 20 years instead of 30 years?
5. What is the difference between monthly and yearly compounding on the final balance?

**Tip:** Small increases in the interest rate or deposit amounts can significantly impact the future value due to the power of compound interest.

Find out how much you will accumulate in a Roth IRA after 30 years with $150 monthly contributions and a 6% annual interest rate compounded monthly. This problem involves key financial concepts like compound interest and annuities. Perfect for students in Grades 9-12.

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