Final answer:
The question involves calculating the initial amount of a bonus invested at a compound interest rate and the total interest earned over time. Given data is insufficient for a precise calculation, but examples highlight the growing impact of compound interest over extended periods and with larger sums of money.
Step-by-step explanation:
The question asks to determine the initial amount of a bonus that Rick placed in an investment earning compound interest and the total interest paid over 9 years, with monthly withdrawals. To solve this, we would typically use the formula for the future value of an annuity due to repeated withdrawals and the fact that the investment is compounded monthly. However, the information provided does not directly give us the exact formula, and calculating it requires more data than offered.
Understanding compound interest is essential as it can lead to significant growth of an investment compared to simple interest. The mentioned examples demonstrate the power of compound interest over time. For example, an initial investment of $100 with a 3-year duration and a specific interest rate could accumulate a certain amount in total compound interest. Compound interest accounts for accumulated interest when calculating new interest, leading to increased returns, especially when starting to save money early in life.
The overall concept emphasizes the impact of starting savings early and allowing the investment to grow through compound interest, which is evident in the examples of investments growing fifteen-fold over 40 years or a bank account's balance doubling after a certain number of years due to interest.