A sum of money doubles itself in 5 years. In how many years will it become four-fold (if interest is compounded)?

This problem can be solved using the rule of 72, which is a simple way to determine how long an investment will take to double, given a fixed annual rate of interest.

1. The rule of 72 states that the time required to double an investment with a certain annual interest rate is approximately 72 divided by that interest rate.

2. In this case, the money doubles in 5 years. So, the interest rate is 72/5 = 14.4% per year.

3. Now, we want to find out how long it will take for the money to become four-fold.

4. Since the money doubles in 5 years, it will double again in another 5 years (because the rate of interest is compounded).

5. Therefore, the money will become four-fold in 5 + 5 = 10 years.

So, the answer is 10 years.