A sum borrowed under compound interest doubles itself in 10 years. When will it become fourfold itself at the same rate of interest?

Answer

To solve the question, we need to determine how long it will take for a sum of money to become four times its original amount under compound interest, given that it doubles in 10 years.

### Step-by-Step Solution:

1. **Understanding the Problem:**
- We know that a sum of money (let's call it P) doubles itself in 10 years. This means that after 10 years, the amount becomes 2P.

2. **Finding the Time to Become Fourfold:**
- To find out when the amount becomes fourfold (4P), we can observe the pattern of how the amount grows under compound interest.
- If it doubles in 10 years (from P to 2P), then in the next 10 years, it will double again.
- Therefore, after another 10 years (which is 20 years in total), the amount will become 4P.

3. **Conclusion:**
- Thus, the time taken for the amount to become fourfold is 20 years.

### Final Answer:
The sum will become fourfold itself in **20 years**.

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