Sumit invested Rs. 50.000 each in two banks for 2 years. The first bank gives simple interest at the rate of 11% per annum. while the other bank gives compound interest, compounded annually at the rate of 10% per annum. How much interest did he earn from the two banks in 2 years?

Options

A. Rs. 21,000
B. Rs. 10,000
C. Rs. 10,500
D. Rs. 21,500

Answer

To solve the problem, we will calculate the interest earned from both banks separately and then sum them up.

### Step 1: Calculate Simple Interest from Bank A
- **Principal (P)** = Rs. 50,000
- **Rate of Interest (R)** = 11% per annum
- **Time (T)** = 2 years

The formula for Simple Interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]

Substituting the values:
\[ SI = \frac{50,000 \times 11 \times 2}{100} \]
\[ SI = \frac{50,000 \times 22}{100} \]
\[ SI = \frac{1,100,000}{100} = 11,000 \]

### Step 2: Calculate Compound Interest from Bank B
- **Principal (P)** = Rs. 50,000
- **Rate of Interest (R)** = 10% per annum
- **Time (T)** = 2 years

The formula for Compound Interest (CI) is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
Where \(A\) is the total amount after time \(T\).

Substituting the values:
\[ A = 50,000 \left(1 + \frac{10}{100}\right)^2 \]
\[ A = 50,000 \left(1 + 0.10\right)^2 \]
\[ A = 50,000 \left(1.10\right)^2 \]
\[ A = 50,000 \times 1.21 = 60,500 \]

Now, to find the Compound Interest:
\[ CI = A - P = 60,500 - 50,000 = 10,500 \]

### Step 3: Calculate Total Interest Earned
Now we will sum the interests earned from both banks:
\[ \text{Total Interest} = SI + CI \]
\[ \text{Total Interest} = 11,000 + 10,500 = 21,500 \]

### Final Answer
The total interest earned from the two banks in 2 years is Rs. 21,500.

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