A sum is invested at compound interest payable annually. The interest in two successive years was 225 and 236.25. Find the rate of interest

Options

A. `2%`
B. `3%`
C. `5%`
D. `9%`

Answer

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

### Step 1: Identify the given values
The interest for the first year (I1) is 225, and the interest for the second year (I2) is 236.25.

### Step 2: Calculate the difference in interest
The difference in interest between the second and first year is:
\[ I2 - I1 = 236.25 - 225 = 11.25 \]

### Step 3: Relate the difference to the rate of interest
The difference in interest (11.25) is the interest earned on the principal amount (P) during the first year (I1). This means that the interest for the second year is the first year's interest plus the additional interest earned due to the rate of interest (r%).

### Step 4: Set up the equation
Since the interest for the first year is 225, we can express the relationship as:
\[ \text{Difference} = \frac{r}{100} \times P \]
Thus, we have:
\[ 11.25 = \frac{r}{100} \times 225 \]

### Step 5: Solve for the rate of interest (r)
Rearranging the equation gives:
\[ r = \frac{11.25 \times 100}{225} \]
Calculating this:
\[ r = \frac{1125}{225} = 5 \]

### Step 6: Conclusion
The rate of interest is:
\[ \text{Rate of Interest} = 5\% \]