In what time a sum will double itself at 12% annual rate of simple interest?

Options

A. 8 Years, 9 months
B. 6 Years, 9 months
C. 8 Years, 4 months
D. 7 Years, 6 months

Answer

To solve the problem of determining the time required for a sum to double itself at a 12% annual rate of simple interest, we can follow these steps:

### Step 1: Understand the concept of Simple Interest
Simple Interest (SI) is calculated using the formula:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
where:
- \( P \) = Principal amount (initial sum of money)
- \( R \) = Rate of interest (annual)
- \( T \) = Time (in years)

### Step 2: Set up the equation for doubling the principal
If the principal amount doubles, the Simple Interest earned will be equal to the principal amount itself. Let’s denote the principal as \( P = x \). Therefore, the Simple Interest when the amount doubles is:
\[ \text{SI} = x \]

### Step 3: Substitute into the Simple Interest formula
Now, substituting into the SI formula, we have:
\[ x = \frac{x \times 12 \times T}{100} \]

### Step 4: Simplify the equation
We can simplify this equation. First, we can cancel \( x \) from both sides (assuming \( x \neq 0 \)):
\[ 1 = \frac{12 \times T}{100} \]

### Step 5: Rearranging to find T
Now, rearranging the equation to solve for \( T \):
\[ T = \frac{100}{12} \]

### Step 6: Calculate T
Calculating \( T \):
\[ T = \frac{100}{12} = \frac{25}{3} \text{ years} \]

### Step 7: Convert years into months
To convert years into months, we multiply by 12:
\[ T = \frac{25}{3} \times 12 = 100 \text{ months} \]

### Final Answer
Thus, the time required for a sum to double itself at a 12% annual rate of simple interest is **100 months**.

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