The following table shows the average returns for some of the largest mutual funds commonly found in retirement plans. (Assume end-of-month deposits and withdrawals and monthly compounding, and assume that the quoted rate of return continues indefinitely.)
Mutual
Fund	Fidelity
Growth
Company	Vanguard
500 Index	PIMCO
Total Return	Vanguard
Total Bond
Market Index
Rate of
Return	15.83%	14.25%	3.77%	3.67%
Type	Stock fund	Stock fund	Bond fund	Bond fund
How much would be accumulated after 30 years in a retirement account invested entirely in the Fidelity stock fund with payments of $500 per month? HINT [See Quick Example 1.] (Round your answer to the nearest cent.)

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!

How much would be accumulated after 30 years in a retirement account invested entirely in the Fidelity stock fund with payments of $500 per month? Assume end-of-month deposits and withdrawals, monthly compounding, and the quoted rate of return continues indefinitely (15.83%).

Learn how to calculate the future value of a retirement investment in the Fidelity Growth Company fund, with monthly payments of $500 and a 15.83% annual return rate. This step-by-step guide includes the future value of an annuity formula and detailed calculations for a 30-year investment period. Ideal for high school or college students learning about compound interest and annuities.

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