Find the compound interset for a sum of ? 9375 in 2 yr, if the rate of interest for the first year is 2% and for the second year is 4%

Options

A. ? 570
B. ? 670
C. ? 770
D. ? 760

Answer

To find the compound interest for a sum of ₹9375 over 2 years with different rates of interest for each year, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Principal Amount (P)**:
- The principal amount is given as ₹9375.

2. **Identify the Rates of Interest**:
- The rate of interest for the first year (R1) is 2%.
- The rate of interest for the second year (R2) is 4%.

3. **Calculate the Amount after the First Year (A1)**:
- The formula to calculate the amount after the first year is:
\[ A_1 = P \times \left(1 + \frac{R_1}{100}\right) \]
- Substitute the values:
\[ A_1 = 9375 \times \left(1 + \frac{2}{100}\right) = 9375 \times \left(1 + 0.02\right) = 9375 \times 1.02 \]
- Calculate:
\[ A_1 = 9375 \times 1.02 = 9555 \]

4. **Calculate the Amount after the Second Year (A2)**:
- Now, use the amount from the first year as the principal for the second year:
\[ A_2 = A_1 \times \left(1 + \frac{R_2}{100}\right) \]
- Substitute the values:
\[ A_2 = 9555 \times \left(1 + \frac{4}{100}\right) = 9555 \times \left(1 + 0.04\right) = 9555 \times 1.04 \]
- Calculate:
\[ A_2 = 9555 \times 1.04 = 9937.2 \]

5. **Calculate the Compound Interest (CI)**:
- The compound interest is given by:
\[ CI = A_2 - P \]
- Substitute the values:
\[ CI = 9937.2 - 9375 = 562.2 \]

### Final Result:
The compound interest for the sum of ₹9375 over 2 years is ₹562.2.

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