A sum of money placed at compound interest doubles itself in 6 years. In how many years will it amount to 16 times itself?

Answer

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

### Step 1: Understand the problem
We know that a sum of money doubles itself in 6 years. We need to find out how many years it will take for the same sum of money to amount to 16 times itself.

**Hint:** Identify the relationship between the time taken to double and the time taken to reach 16 times.

### Step 2: Calculate the doubling process
If the initial amount is \( P \), after 6 years it becomes \( 2P \). After another 6 years (total of 12 years), it will double again:
- After 12 years: \( 2P \) doubles to \( 4P \).

**Hint:** Each 6-year period results in the amount doubling.

### Step 3: Continue the doubling process
Continuing this process:
- After 18 years (3 periods of 6 years): \( 4P \) doubles to \( 8P \).
- After 24 years (4 periods of 6 years): \( 8P \) doubles to \( 16P \).

**Hint:** Keep track of how many 6-year periods it takes to reach 16 times the original amount.

### Step 4: Calculate the total time taken
Since it takes 4 periods of 6 years to reach \( 16P \), we can calculate the total time:
\[ 4 \times 6 = 24 \text{ years} \]

**Hint:** Multiply the number of periods by the duration of each period to find the total time.

### Conclusion
Therefore, it will take **24 years** for the sum of money to amount to 16 times itself.

**Final Answer:** 24 years

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