A sum becomes two times in 7 years at compound interest. In how many years the same sum will become 16 times?

Options

A. 21
B. 28
C. 35
D. 19

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the Problem
We know that a sum of money (let's call it P) becomes double (2P) in 7 years at compound interest. We need to determine how many years it will take for the same sum (P) to become 16 times (16P).

**Hint:** Identify the relationship between the time taken and the multiples of the principal amount.

### Step 2: Determine the Doubling Time
From the information given, we know that:
- In 7 years, the amount becomes 2P (double the principal).

**Hint:** Recognize that if it doubles in 7 years, it will continue to double in subsequent periods of 7 years.

### Step 3: Calculate the Time to Reach 4P
If it doubles again in another 7 years:
- After 14 years, the amount will become 4P.

**Hint:** Keep track of how many times the amount doubles and the corresponding time intervals.

### Step 4: Calculate the Time to Reach 8P
Continuing this pattern, if it doubles again in another 7 years:
- After 21 years, the amount will become 8P.

**Hint:** Each doubling takes the same amount of time (7 years).

### Step 5: Calculate the Time to Reach 16P
If it doubles once more in another 7 years:
- After 28 years, the amount will become 16P.

**Hint:** Add the time intervals together to find the total time taken to reach 16 times the principal.

### Final Answer
Thus, it will take a total of **28 years** for the sum to become 16 times the principal at compound interest.

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