Final answer:
Using the adapted Rule of 72 for monthly compounding, dividing 72 by the monthly interest rate of 0.75% (9% annual interest rate divided by 12 months), it would take approximately 96 months, or 8 years, for an investment to double at a 9% interest rate compounded monthly.
Step-by-step explanation:
Understanding the Time to Double an Investment
To calculate how long it would take for an investment to double in value with a 9% annual interest rate compounded monthly, we use the Rule of 72. This rule is a simple way to estimate the number of years required to double the invested money at a fixed annual rate of interest.
By dividing 72 by the annual interest rate, you can get a rough estimate. However, since the interest is compounded monthly we adapt the Rule of 72 by dividing it by the monthly interest rate, which is the annual rate divided by 12.
First, we convert the annual interest rate to a monthly interest rate: 9% annually is 0.75% per month (9% / 12 months). Then we apply the adapted Rule of 72: Divide 72 by 0.75 to find the number of months it takes to double the investment, which equals 96 months.
To convert this to years, divide 96 months by 12, resulting in 8 years. Therefore, at a 9% compounded monthly interest, it would take approximately 8 years for the investment to double.
It's important to note that the Rule of 72 is an approximation and actual results can vary especially with different compounding periods, but it provides a quick and useful estimate.