If you put $1500 each quarter in your Roth IRA account that earns 10% per year, how much money will you have after 30 years? Round your answer to 2 decimal places.

To calculate how much money you will have after 30 years, given that you are contributing $1,500 each quarter to your Roth IRA and it earns 10% per year, we can use the future value of an annuity formula:

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

Where:
- $ P = 1500 $ is the quarterly contribution,
- $ r = 0.10 $ is the annual interest rate (10%),
- $ n = 4 $ is the number of compounding periods per year (quarterly),
- $ t = 30 $ is the number of years.

### Step-by-Step Calculation:

1. **Quarterly interest rate:**
   \[
   \frac{r}{n} = \frac{0.10}{4} = 0.025
   \]
   
2. **Number of total periods (quarters):**
   \[
   nt = 4 \times 30 = 120
   \]
   
3. **Calculate the future value:**
   \[
   FV = 1500 \times \frac{(1 + 0.025)^{120} - 1}{0.025}
   \]

   \[
   FV = 1500 \times \frac{(1.025)^{120} - 1}{0.025}
   \]

4. **Simplify and calculate:**

   First, calculate $ (1.025)^{120} $:
   \[
   (1.025)^{120} \approx 11.468
   \]

   Now plug this into the formula:
   \[
   FV = 1500 \times \frac{11.468 - 1}{0.025}
   \]
   \[
   FV = 1500 \times \frac{10.468}{0.025}
   \]
   \[
   FV = 1500 \times 418.72
   \]
   \[
   FV \approx 628,080.00
   \]

### Conclusion:
After 30 years, you will have approximately **$628,080.00** in your Roth IRA account.

Would you like more details, or do you have any further questions?

Here are 5 related questions to explore:
1. How would the future value change if the interest rate was 8% instead of 10%?
2. What if you contributed monthly instead of quarterly?
3. How does inflation affect the real value of this future amount?
4. What happens if you withdraw from the account before the 30 years are up?
5. How would changing the contribution amount to $2000 per quarter affect the future value?

**Tip:** Regular contributions and compound interest significantly increase the future value of an investment!

Learn how to calculate the future value of contributing $1500 each quarter to a Roth IRA account with an annual interest rate of 10% over 30 years. This step-by-step solution covers the formula for future value of annuities, compound interest calculations, and exponential growth. Ideal for Grades 11-12 and college students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation