A sum of money at compound interest amounts thrice of itself in 3 years. In how many years it will be 9 times of itself ?

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the Given Information
We know that a sum of money amounts to three times itself in 3 years. This means if we let the initial amount be \( P \), then after 3 years it becomes \( 3P \).

### Step 2: Identify the Relationship in Compound Interest
In compound interest, the amount grows exponentially. If an amount becomes \( 3P \) in 3 years, we can use this information to find out how long it will take to become \( 9P \).

### Step 3: Calculate the Amount After Another 3 Years
Since the amount becomes \( 3P \) in 3 years, we can find out what happens in the next 3 years. The amount \( 3P \) will again grow by the same factor (which is 3) in the next 3 years.

\[ \text{Amount after another 3 years} = 3P \times 3 = 9P \]

### Step 4: Calculate the Total Time
Since it takes 3 years to reach \( 3P \) and another 3 years to reach \( 9P \), we can add these two time periods together.

\[ \text{Total time} = 3 \text{ years} + 3 \text{ years} = 6 \text{ years} \]

### Conclusion
Thus, it will take a total of **6 years** for the sum of money to become 9 times itself.

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