A sum of Rs. 16000 earns a simple interest of Rs. 2560 in 2 years. Find the rate of interest per annum.

Answer

To find the rate of interest per annum for the given problem, we can follow these steps:

### Step 1: Write down the formula for Simple Interest (SI)
The formula for calculating Simple Interest is:
\[ \text{SI} = \frac{\text{Principal} \times \text{Rate} \times \text{Time}}{100} \]

### Step 2: Identify the given values
From the question, we have:
- Principal (P) = Rs. 16,000
- Simple Interest (SI) = Rs. 2,560
- Time (T) = 2 years

### Step 3: Substitute the known values into the formula
We need to find the Rate (R). Substituting the known values into the formula gives us:
\[ 2560 = \frac{16000 \times R \times 2}{100} \]

### Step 4: Rearrange the equation to solve for R
To isolate R, we can rearrange the equation:
\[ R = \frac{2560 \times 100}{16000 \times 2} \]

### Step 5: Simplify the equation
Now, we can simplify the right side:
1. Calculate the denominator:
\[ 16000 \times 2 = 32000 \]
2. Now substitute this back into the equation:
\[ R = \frac{2560 \times 100}{32000} \]

### Step 6: Cancel out the zeros
We can simplify further by canceling out the zeros:
\[ R = \frac{256 \times 10}{3200} \]

### Step 7: Divide the numbers
Now, we can divide:
1. Divide 256 by 32:
\[ 256 \div 32 = 8 \]
2. Divide 10 by 10:
\[ 10 \div 10 = 1 \]
So, we have:
\[ R = 8\% \]

### Final Answer
The rate of interest per annum is **8%**.

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