A sum of money doubles itself in 10 years at simple interest. What is the rate of interest?

Options

A. `5%`
B. `8%`
C. `10%`
D. `2%`

Answer

To find the rate of interest when a sum of money doubles itself in 10 years at simple interest, we can follow these steps:

### Step 1: Understand the problem
We know that the sum of money doubles in 10 years. This means if we start with a principal amount (let's denote it as P), after 10 years, the total amount (A) will be 2P.

### Step 2: Set up the equation for Simple Interest
The formula for Simple Interest (SI) is given by:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \(SI\) = Simple Interest
- \(P\) = Principal amount
- \(R\) = Rate of interest per annum
- \(T\) = Time in years

### Step 3: Calculate the Simple Interest
Since the amount doubles, the Simple Interest earned in 10 years will be equal to the principal amount:
\[ SI = A - P = 2P - P = P \]

### Step 4: Substitute values into the SI formula
We know:
- \(SI = P\)
- \(T = 10\) years

Substituting these into the SI formula:
\[ P = \frac{P \times R \times 10}{100} \]

### Step 5: Simplify the equation
We can divide both sides by \(P\) (assuming \(P \neq 0\)):
\[ 1 = \frac{R \times 10}{100} \]

### Step 6: Solve for R
Now, multiply both sides by 100:
\[ 100 = R \times 10 \]
Now, divide both sides by 10:
\[ R = 10 \]

### Conclusion
The rate of interest is \(10\%\).