How much do you need to invest every month to reach a savings goal of $600,000 at the end of 20 years, if you invest in an annuity that pays 3% interest, compounded monthly? Enter your answer rounded to the nearest dollar.

To find how much you need to invest every month to reach a savings goal of $600,000 at the end of 20 years, we use the **future value of an annuity formula**, since the investment is made regularly with interest being compounded monthly:

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

Where:
- $FV$ is the future value of the annuity, which is $600,000.
- $P$ is the monthly payment (what we want to find).
- $r$ is the monthly interest rate (annual interest rate divided by 12).
- $n$ is the total number of payments (years multiplied by 12).

Given:
- The interest rate is 3% annually, so the monthly interest rate is:

\[
r = \frac{3\%}{12} = \frac{0.03}{12} = 0.0025
\]

- The total number of payments over 20 years is:

\[
n = 20 \times 12 = 240 \, \text{months}
\]

Now we can plug these values into the future value of annuity formula and solve for $P$.

\[
600,000 = P \times \frac{(1 + 0.0025)^{240} - 1}{0.0025}
\]

Let me calculate this step-by-step.You will need to invest approximately **$1,828** every month to reach a savings goal of $600,000 at the end of 20 years, with a 3% interest rate compounded monthly.

Would you like more details or have any questions?

Here are some related questions to explore:
1. What would the monthly payment be if the interest rate increased to 4%?
2. How would the payment change if the goal was $1,000,000 instead?
3. What if the investment period was only 15 years instead of 20?
4. How does changing from monthly to quarterly compounding affect the payment?
5. How is the future value affected if you can only invest $1,500 per month?

**Tip:** Compounding more frequently (e.g., monthly vs. annually) helps to grow your investments faster over time.

Discover how to calculate the monthly investment needed to reach a $600,000 savings goal in 20 years, with a 3% interest rate compounded monthly. Using the future value of an annuity formula, you'll learn the key steps involved in this financial calculation. Suitable for high school and college students.

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