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
Type	Stock fund	Stock fund	Bond fund	Bond fund
Rate of
Return	30.31%	17.98%	3.63%	3.10%
How much would be accumulated after 25 years in a retirement account invested entirely in the Vanguard 500 stock fund with payments of $320 per month? HINT [See Quick Example 1.] (Round your answer to the nearest cent.)
$

To solve this problem, we need to calculate the future value of a retirement account with monthly contributions using the given rate of return and the time period. The future value of an annuity formula is used here, which assumes regular payments with interest being compounded at a specific rate.

The formula for the future value $FV$ of an annuity compounded monthly is:

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

Where:
- $P$ = monthly payment = $320
- $r$ = monthly interest rate (annual rate divided by 12)
- $n$ = total number of payments (months)
- $t$ = number of years

### Step 1: Identify the inputs
- Rate of return for Vanguard 500 Index = 17.98% per year
- Monthly interest rate $r = \frac{17.98\%}{12} = 0.1798 / 12 = 0.0149833$
- Total number of payments over 25 years $n = 25 \times 12 = 300$ months
- Monthly payment $P = 320$

### Step 2: Plug the values into the formula
\[
FV = 320 \times \left( \frac{(1 + 0.0149833)^{300} - 1}{0.0149833} \right)
\]

Let’s compute this step-by-step. I’ll calculate the exact result.The accumulated amount after 25 years in the retirement account, invested entirely in the Vanguard 500 Index fund with monthly payments of $320, would be approximately **$1,828,826.47**.

Would you like further details or have any questions about the calculations? Here are 5 related questions to deepen your understanding:

1. How does changing the monthly payment affect the final accumulated amount?
2. What if the rate of return changes to a different percentage over time?
3. How would the result differ if the investment was in a bond fund with a lower return?
4. How does the compounding frequency (e.g., monthly vs. yearly) influence the outcome?
5. How can inflation impact the real value of the accumulated funds over 25 years?

**Tip:** The longer you leave your investments to compound, the more exponential growth you’ll experience—this is known as the "power of compounding."

How much would be accumulated after 25 years in a retirement account invested entirely in the Vanguard 500 stock fund with payments of $320 per month? Assume end-of-month deposits and withdrawals, monthly compounding, and that the quoted rate of return (17.98%) continues indefinitely.

Calculate the future value of a retirement account invested in the Vanguard 500 stock fund with $320 monthly payments over 25 years. This solution uses the future value of annuity formula and compound interest to determine an accumulation of approximately $1,828,826.47, assuming a 17.98% annual return.

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