At what rate of interest per annum will a sum double itself in 8 years ?

Answer

To find the rate of interest per annum at which a sum will double itself in 8 years, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We need to find the rate of interest (R) at which a principal amount (P) will double in 8 years. If the principal amount is P, then the amount after 8 years will be 2P.

2. **Define Simple Interest**: The formula for Simple Interest (SI) is given by:
\[ SI = \frac{P \times R \times T}{100} \]
where:
- \( P \) = Principal amount
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

3. **Calculate Simple Interest for Doubling**: Since the amount doubles, the Simple Interest earned in 8 years will be:
\[ SI = 2P - P = P \]

4. **Substitute Values into the SI Formula**: Now we can substitute the values into the SI formula. We know that:
- \( SI = P \)
- \( T = 8 \) years

Plugging these into the formula gives:
\[ P = \frac{P \times R \times 8}{100} \]

5. **Cancel Out P**: Since \( P \) is common on both sides of the equation, we can cancel it out (assuming \( P \neq 0 \)):
\[ 1 = \frac{R \times 8}{100} \]

6. **Rearranging the Equation**: To find \( R \), we can rearrange the equation:
\[ R \times 8 = 100 \]

7. **Solve for R**: Now, divide both sides by 8 to isolate \( R \):
\[ R = \frac{100}{8} = 12.5 \]

8. **Conclusion**: Therefore, the rate of interest per annum at which a sum will double itself in 8 years is:
\[ R = 12.5\% \]