In what time will a sum double itself at 8% per annum simple interest ?

Options

A. 12
B. 10
C. 12 1/2
D. none of these

Answer

To solve the problem of determining how long it will take for a sum to double itself at an 8% per annum simple interest rate, 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 per annum
- \( T \) = Time in years

### Step 2: Set Up the Equation
Since we want the sum to double, the total amount (Principal + Interest) should equal \( 2P \). Thus, the interest earned should equal the principal:
\[ \text{SI} = P \]

### Step 3: Substitute SI in the Formula
Using the formula for Simple Interest, we can substitute:
\[ P = \frac{P \times R \times T}{100} \]

### Step 4: Cancel Out the Principal
Since \( P \) is common on both sides, we can cancel it out (assuming \( P \neq 0 \)):
\[ 1 = \frac{R \times T}{100} \]

### Step 5: Substitute the Rate of Interest
Now, substitute \( R = 8 \):
\[ 1 = \frac{8 \times T}{100} \]

### Step 6: Rearrange the Equation to Solve for Time
Rearranging gives:
\[ T = \frac{100}{8} \]

### Step 7: Simplify the Expression
Now, simplify \( \frac{100}{8} \):
\[ T = 12.5 \text{ years} \]

### Conclusion
Thus, the time required for the sum to double itself at an 8% per annum simple interest rate is **12.5 years**.

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