At a deposit of Rs. 2,000 a bank returns Rs. 3,000 after 5 years. What is the percentage rate of interest?

Options

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

Answer

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

### Step 1: Identify the principal amount and the total amount returned
- **Principal Amount (P)**: Rs. 2,000
- **Total Amount Returned (A)**: Rs. 3,000

### Step 2: Calculate the interest earned
- **Interest (I)**: This can be calculated using the formula:
\[ I = A - P \]
Substituting the values:
\[ I = 3000 - 2000 = 1000 \text{ Rs.} \]

### Step 3: Identify the time period
- **Time (T)**: 5 years

### Step 4: Use the formula for Simple Interest
The formula for Simple Interest is:
\[ I = \frac{P \times R \times T}{100} \]
Where:
- \( I \) = Interest
- \( P \) = Principal
- \( R \) = Rate of Interest (in percentage)
- \( T \) = Time (in years)

### Step 5: Substitute the known values into the formula
We know \( I = 1000 \), \( P = 2000 \), and \( T = 5 \). Substituting these values into the formula gives:
\[ 1000 = \frac{2000 \times R \times 5}{100} \]

### Step 6: Simplify the equation
To simplify, we can multiply both sides by 100:
\[ 1000 \times 100 = 2000 \times R \times 5 \]
This simplifies to:
\[ 100000 = 10000R \]

### Step 7: Solve for R
Now, divide both sides by 10000:
\[ R = \frac{100000}{10000} = 10 \]

### Step 8: State the percentage rate of interest
Thus, the percentage rate of interest is:
\[ R = 10\% \]

### Final Answer
The percentage rate of interest is **10%**.

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