A sum of money invested at compound interest doubles itself in 6 years. At the same rate of interest it will amount to eight times of itself in:

Options

A. 15 years
B. 12 years
C. 18 years
D. 10 years

Answer

To solve the problem, we need to determine how long it will take for a sum of money to amount to eight times itself at the same rate of compound interest, given that it doubles in 6 years.

### Step-by-Step Solution:

1. **Understanding the Doubling Time**:
- We know that the principal amount (let's denote it as P) doubles in 6 years. This means that after 6 years, the amount becomes 2P.

2. **Calculating Further Doublings**:
- After another 6 years (which is a total of 12 years), the amount will double again. Therefore, the amount after 12 years will be:
\[ 2P \text{ (after 6 years)} \rightarrow 4P \text{ (after another 6 years)} \]

3. **Continuing the Doubling Process**:
- After another 6 years (which is a total of 18 years), the amount will double once more. Thus, the amount after 18 years will be:
\[ 4P \text{ (after 12 years)} \rightarrow 8P \text{ (after another 6 years)} \]

4. **Conclusion**:
- Therefore, it takes a total of 18 years for the sum of money to amount to eight times itself (8P).

### Final Answer:
The sum of money will amount to eight times itself in **18 years**.

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