In what time does a sum of money becomes 3.6 times of itself at simple interest rate of 13% per annum.

Answer

To solve the problem step by step, we will use the formula for simple interest and the relationship between principal, amount, and interest.

### Step 1: Understand the relationship between Principal, Amount, and Simple Interest
The amount (A) at simple interest is given by the formula:
\[ A = P + SI \]
where:
- \( A \) is the amount after time \( T \),
- \( P \) is the principal amount,
- \( SI \) is the simple interest.

### Step 2: Set up the equation
In this problem, we know that the amount becomes 3.6 times the principal. Therefore:
\[ A = 3.6P \]

### Step 3: Write the formula for Simple Interest
The simple interest (SI) can be calculated using the formula:
\[ SI = \frac{P \times R \times T}{100} \]
where:
- \( R \) is the rate of interest,
- \( T \) is the time in years.

### Step 4: Substitute the values into the equation
Substituting the expression for SI into the amount equation:
\[ 3.6P = P + \frac{P \times R \times T}{100} \]

Given that \( R = 13\% \), we can substitute this value:
\[ 3.6P = P + \frac{P \times 13 \times T}{100} \]

### Step 5: Simplify the equation
Now, we can simplify the equation:
\[ 3.6P - P = \frac{P \times 13 \times T}{100} \]
\[ 2.6P = \frac{P \times 13 \times T}{100} \]

### Step 6: Cancel out \( P \) from both sides
Assuming \( P \neq 0 \), we can divide both sides by \( P \):
\[ 2.6 = \frac{13T}{100} \]

### Step 7: Solve for \( T \)
Now, we can solve for \( T \):
\[ 2.6 \times 100 = 13T \]
\[ 260 = 13T \]
\[ T = \frac{260}{13} \]
\[ T = 20 \]

### Conclusion
The time required for the sum of money to become 3.6 times itself at a simple interest rate of 13% per annum is **20 years**.

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