A person deposits Rs. 7000 rupees for 2 years at 8% per annum on simple interest and he deposits Rs. 10,000 for the same rate and same time on compounded interest. Then find the total interest earned by the person after 2 years.

Options

A. Rs. 2784
B. Rs. 2460
C. Rs. 2889
D. Rs. 2680

Answer

To solve the problem, we need to calculate the simple interest (SI) earned on the first deposit and the compound interest (CI) earned on the second deposit, and then sum both interests to find the total interest earned.

### Step-by-Step Solution:

1. **Calculate Simple Interest (SI) for Rs. 7000:**
- Formula for Simple Interest:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
- Where:
- \( P = 7000 \) (Principal)
- \( R = 8 \) (Rate of interest)
- \( T = 2 \) (Time in years)
- Substitute the values:
\[ \text{SI} = \frac{7000 \times 8 \times 2}{100} = \frac{112000}{100} = 1120 \]
- So, the Simple Interest earned is **Rs. 1120**.

2. **Calculate Compound Interest (CI) for Rs. 10,000:**
- Formula for Compound Interest:
\[ \text{Amount} = P \left(1 + \frac{R}{100}\right)^T \]
- Then, CI can be calculated as:
\[ \text{CI} = \text{Amount} - P \]
- Where:
- \( P = 10000 \) (Principal)
- \( R = 8 \) (Rate of interest)
- \( T = 2 \) (Time in years)
- Substitute the values to find the amount:
\[ \text{Amount} = 10000 \left(1 + \frac{8}{100}\right)^2 = 10000 \left(1 + 0.08\right)^2 = 10000 \times (1.08)^2 \]
- Calculate \( (1.08)^2 \):
\[ (1.08)^2 = 1.1664 \]
- Now calculate the amount:
\[ \text{Amount} = 10000 \times 1.1664 = 11664 \]
- Now calculate CI:
\[ \text{CI} = 11664 - 10000 = 1664 \]
- So, the Compound Interest earned is **Rs. 1664**.

3. **Calculate Total Interest Earned:**
- Total Interest = SI + CI
- Substitute the values:
\[ \text{Total Interest} = 1120 + 1664 = 2784 \]

### Final Answer:
The total interest earned by the person after 2 years is **Rs. 2784**.