If the compound interest for the 3rd and 4th year on a certain principal is ₹ 125 and Rs 135 respectively, what is the rate of interest (in %)?

Options

A. 9
B. 10
C. 8
D. 12

Answer

To find the rate of interest based on the compound interest for the 3rd and 4th years, we can follow these steps:

### Step 1: Understand the given information
We know the compound interest (CI) for the 3rd year is ₹125 and for the 4th year is ₹135.

### Step 2: Calculate the difference in compound interest between the 4th year and the 3rd year
To find the rate of interest, we first need to calculate the difference in compound interest between the two years:
\[ \text{Difference} = \text{CI for 4th year} - \text{CI for 3rd year} = 135 - 125 = 10 \]

### Step 3: Relate the difference to the principal and rate of interest
The difference in compound interest between two consecutive years is equal to the interest on the principal for the previous year (which is the CI for the 3rd year). Therefore, we can set up the following equation:
\[ \text{Difference} = \text{CI for 3rd year} \times \frac{r}{100} \]
Where \( r \) is the rate of interest.

### Step 4: Substitute the known values into the equation
Substituting the values we have:
\[ 10 = 125 \times \frac{r}{100} \]

### Step 5: Solve for the rate of interest \( r \)
To isolate \( r \), we can rearrange the equation:
\[ r = \frac{10 \times 100}{125} \]
\[ r = \frac{1000}{125} \]
\[ r = 8 \]

### Step 6: Conclusion
The rate of interest is \( 8\% \).