To solve this question, we need to understand the concept of compound interest (CI). Compound interest is the interest calculated on both the principal amount and the accumulated interest from previous periods.

Given that a certain sum of money is doubled in 4 years, we can assume the initial principal amount as P. After 4 years, the amount will become 2P.

To find out how many years it will take for the amount to become fourfold, we need to determine the time required for the principal amount to double twice.

Let's break down the steps to solve the problem:

Step 1: Understand the given information
- Initial principal amount (P) doubles in 4 years and becomes 2P.

Step 2: Determine the relationship between the principal amount and time
- We can use the compound interest formula to find the relationship between the principal amount, time, and interest rate.
- The formula for compound interest is A = P(1 + r/n)^(nt), where:
- A is the final amount
- P is the principal amount
- r is the annual interest rate (expressed as a decimal)
- n is the number of times interest is compounded per year
- t is the time in years

Step 3: Determine the interest rate and compounding frequency
- The interest rate and compounding frequency are not given in the question. However, since we are not provided with any specific values, we can assume that the interest is compounded annually (n = 1) and the interest rate is constant.

Step 4: Set up the equation
- We know that after 4 years, the amount becomes 2P.
- Plugging these values into the compound interest formula, we get:
- 2P = P(1 + r/1)^(1*4)
- Simplifying the equation, we have:
- 2 = (1 + r)^4

Step 5: Solve for the interest rate
- To solve for the interest rate, we can take the fourth root of both sides of the equation.
- Taking the fourth root, we get:
- 1 + r = ∛2
- r = ∛2 - 1

Step 6: Determine the time required for the amount to become fourfold
- Now that we have the interest rate (r), we can use it to find the time required for the amount to become fourfold.
- Plugging the values into the compound interest formula, we get:
- 4P = P(1 + (∛2 - 1)/1)^(1*t)
- Simplifying the equation, we have:
- 4 = (∛2)^t

Step 7: Solve for the time
- To solve for the time (t), we can take the logarithm of both sides of the equation.
- Taking the logarithm, we get:
- log(4) = log((∛2)^t)
- Simplifying the equation, we have:
- log(4) = t * log(∛2)
- t = log(4) / log(∛2)

Step 8: Calculate the time
- Using a calculator, we can find the value of t.
- Evaluating the expression, we get:
- t ≈ 7.96

Therefore, the amount