On a sum of Rs. 6875, find difference between second year and third year C.I if rate of interest is 20% per Annum?

Options

A. Rs. 275
B. Rs. 300
C. Rs. 330
D. Rs. 325

Answer

To find the difference between the second year and third year compound interest on a sum of Rs. 6875 at a rate of 20% per annum, we can follow these steps:

### Step 1: Calculate the amount at the end of the first year.
The formula for compound interest is:
\[ A = P(1 + r)^n \]
Where:
- \( A \) = Amount after \( n \) years
- \( P \) = Principal amount (initial investment)
- \( r \) = Rate of interest (in decimal)
- \( n \) = Number of years

For the first year:
- \( P = 6875 \)
- \( r = 20\% = 0.20 \)
- \( n = 1 \)

Calculating:
\[ A_1 = 6875(1 + 0.20)^1 = 6875 \times 1.20 = 8250 \]

### Step 2: Calculate the amount at the end of the second year.
Using the amount from the first year as the principal for the second year:
- \( P = 8250 \)
- \( n = 1 \)

Calculating:
\[ A_2 = 8250(1 + 0.20)^1 = 8250 \times 1.20 = 9900 \]

### Step 3: Calculate the amount at the end of the third year.
Using the amount from the second year as the principal for the third year:
- \( P = 9900 \)
- \( n = 1 \)

Calculating:
\[ A_3 = 9900(1 + 0.20)^1 = 9900 \times 1.20 = 11880 \]

### Step 4: Calculate the compound interest for the second and third years.
- Compound Interest for the second year:
\[ CI_2 = A_2 - A_1 = 9900 - 8250 = 1650 \]
- Compound Interest for the third year:
\[ CI_3 = A_3 - A_2 = 11880 - 9900 = 1980 \]

### Step 5: Find the difference between the third year and second year compound interest.
\[ \text{Difference} = CI_3 - CI_2 = 1980 - 1650 = 330 \]

### Final Answer:
The difference between the second year and third year compound interest is Rs. 330.

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