At compound interest , if a certain sum of money doubles in n years , then the amount will be four fold in :

Options

A. `n^2` years
B. `2n^2` years
C. 2n years
D. 4n years

Answer

To solve the problem, we need to determine how many years it will take for a certain sum of money to quadruple (become four times) if it doubles in \( n \) years at compound interest.

### Step-by-Step Solution:

1. **Understanding Doubling**:
- If a sum of money doubles in \( n \) years, it means that after \( n \) years, the amount becomes \( 2P \) where \( P \) is the principal amount.

2. **Finding Time to Double**:
- We know that the time taken to double the amount is \( n \) years.

3. **Finding Time to Quadruple**:
- To find out how long it takes for the amount to become four times the original (quadruple), we can use the fact that quadrupling can be seen as two doublings.
- If the amount doubles in \( n \) years, then it will double again in another \( n \) years.

4. **Calculating Total Time**:
- Therefore, the total time to quadruple the amount will be:
\[ n + n = 2n \text{ years} \]

5. **Conclusion**:
- Thus, if a certain sum of money doubles in \( n \) years, it will become fourfold in \( 2n \) years.

### Final Answer:
The amount will be fourfold in \( 2n \) years.

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