Find the difference between CI of 3rd year and 2nd year on 6000 at the rate of 5%?

Options

A. ₹ 12.75
B. ₹ 16.75
C. ₹ 15.75
D. ₹ 14.75

Answer

To find the difference between the compound interest (CI) earned in the 3rd year and the 2nd year on an amount of 6000 at a rate of 5%, we can follow these steps:

### Step 1: Calculate the Compound Interest for the 2nd Year
The formula for calculating compound interest for a specific year is:
\[ \text{CI} = P \times \left(1 + \frac{r}{100}\right)^n - P \]
Where:
- \( P \) = Principal amount
- \( r \) = Rate of interest
- \( n \) = Number of years

For the 2nd year:
- Principal amount \( P = 6000 \)
- Rate of interest \( r = 5\% \)
- Number of years \( n = 2 \)

Calculating the total amount after 2 years:
\[ A = 6000 \times \left(1 + \frac{5}{100}\right)^2 \]
\[ A = 6000 \times (1.05)^2 \]
\[ A = 6000 \times 1.1025 = 6615 \]

Now, the CI for the 2nd year is:
\[ \text{CI}_{2nd} = A - P = 6615 - 6000 = 615 \]

### Step 2: Calculate the Compound Interest for the 3rd Year
Now, we will calculate the total amount after 3 years:
\[ A = 6000 \times \left(1 + \frac{5}{100}\right)^3 \]
\[ A = 6000 \times (1.05)^3 \]
\[ A = 6000 \times 1.157625 = 6945.75 \]

Now, the CI for the 3rd year is:
\[ \text{CI}_{3rd} = A - \text{Total amount after 2 years} \]
\[ \text{CI}_{3rd} = 6945.75 - 6615 = 330.75 \]

### Step 3: Find the Difference Between CI of 3rd Year and 2nd Year
Now, we can find the difference:
\[ \text{Difference} = \text{CI}_{3rd} - \text{CI}_{2nd} \]
\[ \text{Difference} = 330.75 - 615 = -284.25 \]

### Final Result
The difference between the compound interest of the 3rd year and the 2nd year is:
\[ \text{Difference} = 330.75 - 615 = -284.25 \]