On rs 8960, the rate of interest for first year is `12 (1)/(2)%` second year is `14 (2)/(7) %` and 3rd year is 10% then find the compound interest for 3 years?

Options

A. ₹ 3712
B. ₹ 3713
C. ₹ 3711
D. ₹ 3710

Answer

To find the compound interest for 3 years on Rs. 8960 with varying rates of interest for each year, we will follow these steps:

### Step 1: Convert the interest rates to decimal form
- For the first year, the interest rate is \( 12 \frac{1}{2}\% = 12.5\% = \frac{12.5}{100} = 0.125 \).
- For the second year, the interest rate is \( 14 \frac{2}{7}\% \). To convert this, we first find the decimal equivalent of \( \frac{2}{7} \approx 0.2857 \), so \( 14 \frac{2}{7}\% \approx 14.2857\% = \frac{14.2857}{100} \approx 0.142857 \).
- For the third year, the interest rate is \( 10\% = \frac{10}{100} = 0.10 \).

### Step 2: Calculate the amount after the first year
Using the formula for compound interest:
\[ A_1 = P \times (1 + r_1) \]
Where \( P = 8960 \) and \( r_1 = 0.125 \):
\[ A_1 = 8960 \times (1 + 0.125) = 8960 \times 1.125 = 10080 \]

### Step 3: Calculate the amount after the second year
Now, we use the amount from the first year as the principal for the second year:
\[ A_2 = A_1 \times (1 + r_2) \]
Where \( r_2 = 0.142857 \):
\[ A_2 = 10080 \times (1 + 0.142857) = 10080 \times 1.142857 \approx 11538.86 \]

### Step 4: Calculate the amount after the third year
Using the amount from the second year as the principal for the third year:
\[ A_3 = A_2 \times (1 + r_3) \]
Where \( r_3 = 0.10 \):
\[ A_3 = 11538.86 \times (1 + 0.10) = 11538.86 \times 1.10 \approx 12692.75 \]

### Step 5: Calculate the total compound interest
The total compound interest (CI) is given by:
\[ CI = A_3 - P \]
Where \( P = 8960 \):
\[ CI = 12692.75 - 8960 = 3732.75 \]

### Final Answer
The compound interest for 3 years is approximately Rs. 3732.75.

---