IF YOU HAD INVESTED $100 IN 1972 IN THE 500 STOCKS OF THE S&P500 INDEX, HOW MUCH WOULD YOU HAVE HAD IN 2018? $401 $500 $1,612 $3,072

To solve this problem, we will follow these steps:

1. ### Break Down the Problem

We need to calculate the growth of an investment of $100 in the S&P 500 from 1972 to 2018. This requires knowing the average annual return of the S&P 500 during that period.

2. ### Relevant Concepts

The compound interest formula is used to find the future value of the investment: $FV = P(1 + r)^n$ where:

• $FV$ = future value of the investment
• $P$ = principal amount (initial investment)
• $r$ = annual interest rate (average return of the investment)
• $n$ = number of years the money is invested

Historical data indicates that the average annual return of the S&P 500 over the long term (including dividends) is approximately 10%.

3. ### Analysis and Detail

1. Initial Investment, $P = 100$ (in dollars)
2. Average Annual Return, $r = 0.10$
3. Number of Years, $n = 2018 - 1972 = 46$

Using the compound interest formula: $FV = 100(1 + 0.10)^{46}$

Now, we calculate $(1 + 0.10)^{46}$: $(1.10)^{46} \approx 32.442$

Now, calculating the future value: $FV = 100 \times 32.442 \approx 3244.21$

4. ### Verify and Summarize

After applying the compound interest formula and calculating:

1. The growth factor is approximately 32.442.
2. The future value of the investment after 46 years is around $3,244.21.

Final Answer

The amount you would have had in 2018 would be approximately $3,244.21**. Among the options given, the closest is **$3,072.