The interest on a certain deposit at 4.5% p.a. is Rs. 202.50 in one year. How much will the additional interest in one year be on the same deposit at 5% p.a. ?

Options

A. Rs. 20.25
B. Rs. 22.50
C. Rs. 25
D. Rs. 42.75

Answer

To solve the problem step by step, we need to find out the principal amount based on the interest earned at 4.5% per annum and then calculate the additional interest at 5% per annum.

### Step 1: Find the Principal Amount
We know that the interest (I) for one year can be calculated using the formula:
\[ I = \frac{P \times R \times T}{100} \]
Where:
- \(I\) = Interest earned
- \(P\) = Principal amount
- \(R\) = Rate of interest per annum
- \(T\) = Time in years

From the question, we have:
- \(I = 202.50\)
- \(R = 4.5\%\)
- \(T = 1\)

Substituting these values into the formula:
\[ 202.50 = \frac{P \times 4.5 \times 1}{100} \]

### Step 2: Rearranging to find P
To find \(P\), we rearrange the equation:
\[ P = \frac{202.50 \times 100}{4.5} \]

### Step 3: Calculate P
Now, we calculate \(P\):
\[ P = \frac{20250}{4.5} = 4500 \]

### Step 4: Calculate Interest at 5% per annum
Now that we have the principal amount \(P = 4500\), we can calculate the interest at 5% per annum for one year:
\[ I_{5\%} = \frac{P \times R \times T}{100} \]
Where:
- \(R = 5\%\)

Substituting the values:
\[ I_{5\%} = \frac{4500 \times 5 \times 1}{100} \]

### Step 5: Calculate I at 5%
Now, we calculate \(I_{5\%}\):
\[ I_{5\%} = \frac{22500}{100} = 225 \]

### Step 6: Calculate Additional Interest
The additional interest earned by moving from 4.5% to 5% is:
\[ \text{Additional Interest} = I_{5\%} - I_{4.5\%} \]
\[ \text{Additional Interest} = 225 - 202.50 = 22.50 \]

### Final Answer
The additional interest in one year on the same deposit at 5% per annum is **Rs. 22.50**.

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