In how much time the principal doubles itself at 12.5% rate of interest?

Options

A. 6 years
B. 7 years
C. 8 years
D. 5 years

Answer

To find out how much time it takes for the principal to double itself at a 12.5% rate of interest, we can use the formula for simple interest. Here’s a step-by-step solution:

### Step 1: Understand the Problem
We need to determine the time (t) it takes for an initial principal amount (P) to double when the interest rate is 12.5%. When the principal doubles, the total amount (A) becomes 2P.

### Step 2: Set Up the Equation
The formula for simple interest is given by:
\[ \text{Simple Interest (SI)} = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal amount
- \( R \) = Rate of interest (12.5% in this case)
- \( T \) = Time in years

Since the amount doubles, the simple interest earned will be equal to the principal:
\[ SI = A - P = 2P - P = P \]

### Step 3: Substitute Values into the Equation
Now we can substitute the values into the simple interest formula:
\[ P = \frac{P \times 12.5 \times T}{100} \]

### Step 4: Simplify the Equation
We can cancel \( P \) from both sides (assuming \( P \neq 0 \)):
\[ 1 = \frac{12.5 \times T}{100} \]

### Step 5: Solve for Time (T)
To isolate \( T \), multiply both sides by 100:
\[ 100 = 12.5 \times T \]
Now divide both sides by 12.5:
\[ T = \frac{100}{12.5} \]

### Step 6: Calculate the Value
Calculating the right side:
\[ T = 8 \]

### Conclusion
It will take 8 years for the principal to double itself at a 12.5% rate of interest.