Final answer:
Using the Rule of 70, an investment of $5,652.20 at a 7% interest rate will double every 10 years, leading to a total of 10 doubling periods over 100 years. After doubling the investment 10 times, the heirs would be able to withdraw approximately $5,769,996.80.
Step-by-step explanation:
The subject in question here is compound interest, which is a common topic in Mathematics, especially when dealing with investments and savings. By employing the Rule of 70, an approximate method to determine how many years it will take for an investment to double given a fixed annual interest rate, we can estimate the doubling time by dividing 70 by the interest rate. In this instance, the interest rate is 7%, so 70 divided by 7 is 10 years. This means the investment will double every 10 years.
To calculate the final amount that the heirs would be able to withdraw after 100 years, we can determine the number of doubling periods within the 100 years. There are 100 years divided by 10 years per period, yielding 10 doubling periods. Starting with $5,652.20, we need to double this amount 10 times:
- Double 1: $5,652.20 × 2 = $11,304.40
- Double 2: $11,304.40 × 2 = $22,608.80
- ... (Continue this process until Double 10)
- Double 10: $2,884,998.40 × 2 = $5,769,996.80
Therefore, at the end of 100 years, the heirs would be able to withdraw approximately $5,769,996.80, rounded to the nearest two decimal places.