Final answer:
The investor's contributions grow to almost ten times their original amount due to the power of compound interest. Compound interest allows both the initial principal and the accumulated interest to earn more interest over time, resulting in exponential growth of the investment, especially with consistent contributions and a good annual rate of return.
Step-by-step explanation:
The question is related to the concept of compound interest, which is pivotal in understanding how investments grow over time. Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods. In the scenario where an investor starts contributing at age 15 and continues until they are 70, contributing a total of $339,000, the reason their investment is worth nearly ten times their contributions at $3,286,310 is due to the power of compound interest.
When money is invested, especially in a well-diversified stock portfolio, it is common to expect a real annual rate of return of around 7%, which is above the inflation rate. This means that not only is the money making interest each year, but that interest is then used to generate more interest the following year. This snowball effect greatly multiplies the value of the initial investment over the long term.
For example, starting with a single investment of $3,000 at a 7% annual rate of return and letting it compound for 40 years without any additional contributions would result in the investment growing to $44,923. With continuous annual contributions and the same compound interest, the result is an even more substantial increase, leading to an eventual wealth that places the individual well within the top 10% of American households in terms of net worth.