Given:
- The amount triples in 4 years under compound interest.
- The interest is being compounded annually.

To Find:
The time it would take for the amount to become 9 times itself.

Solution:

Step 1: Understand the Problem
We need to find the time it takes for the amount to become 9 times itself. Let's assume the principal amount is P and the rate of interest is r.

Step 2: Formulate the Compound Interest Formula
The compound interest formula is given by:
A = P(1 + r/n)^(nt)

Where:
A = Final amount
P = Principal amount
r = Annual interest rate (in decimal form)
n = Number of times the interest is compounded per year
t = Number of years

Step 3: Solve the Problem
Let's assume the initial amount is A1 and the time taken to triple the amount is t1 (which is given as 4 years).
Using the compound interest formula, we have:
A1 = P(1 + r)^t1

We are given that the amount triples in 4 years, which means A1 = 3P.
Therefore, 3P = P(1 + r)^4

Simplifying the equation, we get:
3 = (1 + r)^4

Now, let's assume the time it takes for the amount to become 9 times itself is t2.
Using the compound interest formula again, we have:
A2 = P(1 + r)^t2

We are given that the amount becomes 9 times itself, which means A2 = 9P.
Therefore, 9P = P(1 + r)^t2

Simplifying the equation, we get:
9 = (1 + r)^t2

Step 4: Solve the Equations
From our previous equations, we have:
(1 + r)^4 = 3 -- Equation 1
(1 + r)^t2 = 9 -- Equation 2

Taking the square root of both sides of Equation 2, we get:
1 + r = 3^(1/2)
1 + r = √3

Now, let's solve Equation 1:
(1 + r)^4 = 3
(√3)^4 = 3
3^2 = 3
9 = 3

Since both sides of Equation 1 are equal, we can say that the rate of interest (r) is 0.

Step 5: Find the Time Taken
Substituting the value of r = 0 in Equation 1, we get:
(1 + 0)^4 = 3
1^4 = 3
1 = 3

Since the equation is not satisfied, we can conclude that the time taken for the amount to become 9 times itself is not possible with the given conditions.

Therefore, there is no valid solution to this problem.

Final Answer:
There is no valid solution.