Final answer:
The initial investments of Mr. Brust and Mr. Kelly cannot be determined from the given expressions for their future asset values. However, the concept of compound interest is crucial for understanding how investments grow over time, and higher interest rates can significantly increase the future value of investments.
Step-by-step explanation:
The question presented relates to the compound interest and future value of investments made by Mr. Brust and Mr. Kelly. While the question asks how much each invested, it inadvertently provides expressions for the projected value of their assets over time, rather than the initial investment amounts. To calculate the initial investment (present value), one would typically use the future value formula: Future Value = Present Value × (1 + Interest Rate)^Number of Periods. However, without the interest rates and specific time frames, we cannot determine the initial investments. Instead, we can discuss the concept of compound interest, as evidenced by provided examples.
An individual investing $3,000 with an annual compound interest rate of 7% for 40 years would end up with approximately $44,923. The power of compound interest shows why starting to save early is crucial. Furthermore, changing the interest rate, as in Yelberton's case from 6% to 9%, significantly impacts the future value of an investment, demonstrating how the rate of return plays a pivotal role in financial planning.