A sum of money doubles itself at compound interest in 15 years in how many years it will become eight times?

Answer

To solve the problem of how many years it will take for a sum of money to become eight times itself at compound interest, given that it doubles in 15 years, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Doubling Time**:
We know that the initial sum of money (let's call it P) doubles in 15 years. This means:
\[ \text{After 15 years} = 2P \]

2. **Continuing the Doubling Process**:
Since the money doubles every 15 years, we can calculate the amount after subsequent periods of 15 years:
- After another 15 years (total of 30 years):
\[ \text{After 30 years} = 2P \times 2 = 4P \]
- After another 15 years (total of 45 years):
\[ \text{After 45 years} = 4P \times 2 = 8P \]

3. **Calculating Total Time**:
To find out how long it takes for the initial sum P to become 8 times itself:
\[ \text{Total time} = 15 \text{ years} + 15 \text{ years} + 15 \text{ years} = 45 \text{ years} \]

Thus, the sum of money will become eight times itself in **45 years**.

### Final Answer:
The answer is **45 years**.

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