The compound interest on a certain sum for two successive years are Rs. 225 and Rs. 238.50. The rate of interest per annum is :

Options

A. (a) 7%
B. (b) 5%
C. (c) 6%
D. (d) 10%

Answer

To find the rate of interest per annum given the compound interest for two successive years, we can follow these steps:

### Step 1: Identify the given values
- Compound Interest for Year 1 (CI1) = Rs. 225
- Compound Interest for Year 2 (CI2) = Rs. 238.50

### Step 2: Calculate the difference in compound interest
- Difference = CI2 - CI1
- Difference = 238.50 - 225 = Rs. 13.50

### Step 3: Relate the difference to the principal and rate of interest
- The difference in compound interest over the two years can be expressed as:
\[ \text{Difference} = \text{Principal} \times \text{Rate} \times \frac{1}{100} \]
The interest for the second year is calculated on the amount at the end of the first year, which includes the interest from the first year.

### Step 4: Set up the equation for the second year
- The interest for the second year can also be expressed as:
\[ \text{CI2} = \text{CI1} + \left(\text{Principal} + \text{CI1}\right) \times \text{Rate} \times \frac{1}{100} \]
However, we can simplify our calculations by using the difference we found.

### Step 5: Calculate the rate of interest
- We can express the difference in terms of the first year's interest:
\[ \frac{\text{Difference}}{\text{CI1}} = \frac{13.50}{225} \]
- To find the rate, we multiply by 100:
\[ \text{Rate} = \frac{13.50}{225} \times 100 \]

### Step 6: Simplify the calculation
- Calculate:
\[ \text{Rate} = \frac{1350}{225} \]
- Dividing both numerator and denominator by 45:
\[ \text{Rate} = \frac{30}{5} = 6\% \]

### Final Answer:
The rate of interest per annum is **6%**.

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