A sum becomes 1.6 times of itself in five years at simple rate of interest. Find rate of interest per annum?

Options

A. 0.1
B. 0.125
C. 0.15
D. 0.12

Explanation

To solve the problem step by step, we will use the information provided in the question and apply the formula for simple interest.

### Step 1: Understand the Problem
We are given that a sum of money (the principal, P) becomes 1.6 times itself in 5 years at a simple rate of interest. We need to find the rate of interest per annum.

### Step 2: Define the Variables
Let:
- Principal (P) = P
- Amount after 5 years = 1.6P
- Time (T) = 5 years

### Step 3: Calculate the Simple Interest
The simple interest (SI) can be calculated using the formula:
\[ \text{SI} = \text{Amount} - \text{Principal} \]
So, we have:
\[ \text{SI} = 1.6P - P = 0.6P \]

### Step 4: Use the Simple Interest Formula
The formula for simple interest is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Where:
- SI = Simple Interest
- P = Principal
- R = Rate of interest per annum
- T = Time in years

### Step 5: Substitute the Known Values
We know:
- SI = 0.6P
- T = 5 years

Substituting these values into the formula gives:
\[ 0.6P = \frac{P \times R \times 5}{100} \]

### Step 6: Simplify the Equation
We can cancel P from both sides (assuming P ≠ 0):
\[ 0.6 = \frac{R \times 5}{100} \]

### Step 7: Rearrange to Solve for R
Now, rearranging the equation to find R:
\[ R \times 5 = 0.6 \times 100 \]
\[ R \times 5 = 60 \]

### Step 8: Calculate R
Now, divide both sides by 5 to find R:
\[ R = \frac{60}{5} = 12 \]

### Step 9: Conclusion
The rate of interest per annum is:
\[ R = 12\% \]