A sum of money doubles itself in 7 years. In how many years it will become 4 times ?

Answer

To solve the problem step by step, we will use the relationship between the time taken for a sum of money to double and the time taken for it to quadruple using the formula provided in the video.

### Step 1: Understand the given information
We know that a sum of money doubles in 7 years. This means:
- A (final amount when doubled) = 2
- T1 (time taken to double) = 7 years

### Step 2: Set up the relationship for quadrupling
We want to find out how long it will take for the same sum of money to become four times its original amount. This means:
- B (final amount when quadrupled) = 4
- T2 (time taken to quadruple) = ?

### Step 3: Use the formula
We will use the formula:
\[ \frac{A - 1}{T1} = \frac{B - 1}{T2} \]
Substituting the values we have:
\[ \frac{2 - 1}{7} = \frac{4 - 1}{T2} \]

### Step 4: Simplify the equation
This simplifies to:
\[ \frac{1}{7} = \frac{3}{T2} \]

### Step 5: Cross-multiply to solve for T2
Cross-multiplying gives us:
\[ 1 \cdot T2 = 3 \cdot 7 \]
\[ T2 = 21 \]

### Step 6: Conclusion
Thus, it will take 21 years for the sum of money to become four times its original amount.

### Final Answer
The sum of money will become four times in **21 years**.

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