A bank returns Rs. 3000 after 5 years on the deposit amount of Rs. 2000. What is per cent rate of simple interest?

Options

A. `20%`
B. `15%`
C. `10%`
D. `5%`

Answer

To find the percent rate of simple interest, we can follow these steps:

### Step 1: Identify the given values
- Amount returned (A) = Rs. 3000
- Principal amount (P) = Rs. 2000
- Time (T) = 5 years

### Step 2: Use the formula for Simple Interest
The formula for the total amount (A) in simple interest is:
\[ A = P + \left( \frac{P \times r \times T}{100} \right) \]
Where:
- A = Total amount after time T
- P = Principal amount
- r = Rate of interest per annum
- T = Time in years

### Step 3: Substitute the known values into the formula
Substituting the values we have:
\[ 3000 = 2000 + \left( \frac{2000 \times r \times 5}{100} \right) \]

### Step 4: Simplify the equation
First, isolate the term containing r:
\[ 3000 - 2000 = \frac{2000 \times r \times 5}{100} \]
This simplifies to:
\[ 1000 = \frac{2000 \times r \times 5}{100} \]

### Step 5: Further simplify the equation
Multiply both sides by 100 to eliminate the fraction:
\[ 1000 \times 100 = 2000 \times r \times 5 \]
This gives:
\[ 100000 = 10000r \]

### Step 6: Solve for r
Now, divide both sides by 10000:
\[ r = \frac{100000}{10000} \]
This simplifies to:
\[ r = 10 \]

### Step 7: State the final answer
Thus, the percent rate of simple interest is:
\[ \text{Rate of interest} = 10\% \text{ per annum} \]