To calculate the future value of an investment with regular payments (such as monthly contributions) and compound interest, we use the future value of an annuity formula:

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

Where:

• $FV$ is the future value of the investment.
• $P$ is the monthly payment (in this case, $500).
• $r$ is the monthly interest rate (which is the annual rate divided by 12).
• $n$ is the total number of payments (number of months over the entire period).

Step-by-step calculation:

1. Monthly interest rate ($r$): The annual rate of return for the Fidelity Growth Company fund is 15.83%, so: $r = \frac{{15.83\%}}{12} = \frac{0.1583}{12} = 0.013192 \text{ per month}$

2. Number of months ($n$): The investment period is 30 years, with monthly payments, so: $n = 30 \times 12 = 360 \text{ months}$

3. Substitute values into the formula: $FV = 500 \times \frac{{(1 + 0.013192)^{360} - 1}}{0.013192}$

4. Simplify the expression: First, calculate $(1 + 0.013192)^{360}$: $(1 + 0.013192)^{360} \approx 82.026$

   Now, subtract 1: $82.026 - 1 = 81.026$

   Finally, divide by $r$: $\frac{81.026}{0.013192} \approx 6140.86$

5. Final calculation: $FV = 500 \times 6140.86 = 3,070,430.16$

So, the amount accumulated after 30 years in the Fidelity Growth Company fund with payments of $500 per month is $3,070,430.16.

Would you like more details or have any other questions?

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Here are 5 related questions you might find helpful:

1. How would the future value change if the interest rate was slightly higher, say 16%?
2. What if you contributed $600 instead of $500 per month?
3. How much would be accumulated if you invested in the Vanguard 500 Index instead?
4. What is the effect of a shorter investment period, say 20 years instead of 30 years?
5. How do bond funds' lower rates affect the total accumulation?

Tip: Even a small change in the interest rate can have a large impact on long-term investments due to compounding!