At what percentage simple interest per annum a certain sum will double in 10 year?
A. 7%
B. 8%
C. 9%
D.10 %

Options

A. B
B. A
C. D
D. C

Answer

To solve the problem of finding the percentage of simple interest per annum at which a certain sum will double in 10 years, we can follow these steps:

### Step 1: Understand the Problem
We need to find the rate of simple interest (R) that will cause an initial sum (P) to double in a given time period (T). If the initial sum is P, then after doubling, the amount will be 2P.

### Step 2: Use the Simple Interest Formula
The formula for calculating simple interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- SI = Simple Interest
- P = Principal amount (initial sum)
- R = Rate of interest per annum
- T = Time in years

### Step 3: Set Up the Equation
Since we want the sum to double, we know that:
\[ SI = 2P - P = P \]
So, we can substitute SI with P in the simple interest formula:
\[ P = \frac{P \times R \times T}{100} \]

### Step 4: Simplify the Equation
We can cancel P from both sides (assuming P is not zero):
\[ 1 = \frac{R \times T}{100} \]

### Step 5: Substitute the Known Values
We know that T = 10 years. Substitute this value into the equation:
\[ 1 = \frac{R \times 10}{100} \]

### Step 6: Solve for R
To find R, we can rearrange the equation:
\[ R \times 10 = 100 \]
\[ R = \frac{100}{10} = 10 \]

### Conclusion
The rate of simple interest required to double the sum in 10 years is **10%**. Therefore, the correct answer is **D. 10%**.

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