In what time does money becomes double at simple interest rate of 12% per annum?

Options

A. `6^(1/3)` Years
B. `6^(2/3)` Years
C. `8^(1/3)` Years
D. `8^(2/3)` Years

Answer

To find out the time it takes for money to double at a simple interest rate of 12% per annum, we can follow these steps:

### Step 1: Understand the Problem
We need to determine the time (T) it takes for an initial amount (Principal, P) to double. When the amount doubles, it becomes 2P.

### Step 2: Use the Simple Interest Formula
The formula for calculating the total amount (A) in simple interest is:
\[ A = P + SI \]
Where:
- \( A \) is the total amount after time \( T \)
- \( P \) is the principal amount
- \( SI \) is the simple interest earned

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 per annum
- \( T \) is the time in years

### Step 3: Set Up the Equation
Since we know that the amount becomes double, we can set up the equation:
\[ 2P = P + SI \]
Substituting the formula for SI:
\[ 2P = P + \frac{P \times 12 \times T}{100} \]

### Step 4: Simplify the Equation
Now, we can simplify the equation:
\[ 2P - P = \frac{P \times 12 \times T}{100} \]
This simplifies to:
\[ P = \frac{P \times 12 \times T}{100} \]

### Step 5: Cancel Out the Principal
Assuming \( P \neq 0 \), we can divide both sides by \( P \):
\[ 1 = \frac{12 \times T}{100} \]

### Step 6: Solve for Time (T)
Now, we can solve for \( T \):
\[ T = \frac{100}{12} \]
\[ T = \frac{25}{3} \]
Converting \( \frac{25}{3} \) to a mixed number gives:
\[ T = 8 \frac{1}{3} \text{ years} \]

### Final Answer
The time it takes for the money to double at a simple interest rate of 12% per annum is **8 years and 1/3 year**.

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