The RBI lends a certain amount to the SBI on simple interest for two years at 20%. The SBI gives this entire amount to Bharti Telecom on compound interest for two years at the same rate annually. Find the percentage earning of the SBI at the end of two years on the entire amount

Options

A. 0.04
B. 3(1/7)%
C. 3(2/7)%
D. 2(6/7)%

Answer

To solve the problem step-by-step, we will follow the process of calculating the simple interest for the amount lent by RBI to SBI, then calculate the compound interest for the amount given by SBI to Bharti Telecom, and finally determine the percentage earning of SBI.

### Step 1: Calculate the Simple Interest for SBI from RBI
The formula for Simple Interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \(P\) = Principal amount (let's assume it is \(X\))
- \(R\) = Rate of interest (20%)
- \(T\) = Time (2 years)

Substituting the values:
\[ SI = \frac{X \times 20 \times 2}{100} = \frac{40X}{100} = 0.4X \]

### Step 2: Calculate the Total Amount to be Paid by SBI to RBI
The total amount (A) that SBI has to pay back to RBI after 2 years is:
\[ A = P + SI = X + 0.4X = 1.4X \]

### Step 3: Calculate the Compound Interest for Bharti Telecom
SBI lends the same amount \(X\) to Bharti Telecom at compound interest for 2 years at the same rate (20%). The formula for Compound Interest (CI) is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
Substituting the values:
\[ A = X \left(1 + \frac{20}{100}\right)^2 = X \left(1 + 0.2\right)^2 = X \left(1.2\right)^2 = X \times 1.44 = 1.44X \]

### Step 4: Calculate the Profit of SBI
The profit earned by SBI is the difference between the amount received from Bharti Telecom and the amount paid to RBI:
\[ \text{Profit} = \text{Amount received from Bharti Telecom} - \text{Amount paid to RBI} \]
\[ \text{Profit} = 1.44X - 1.4X = 0.04X \]

### Step 5: Calculate the Percentage Earning of SBI
The percentage earning can be calculated using the formula:
\[ \text{Percentage Earning} = \left(\frac{\text{Profit}}{\text{Amount paid to RBI}}\right) \times 100 \]
Substituting the values:
\[ \text{Percentage Earning} = \left(\frac{0.04X}{1.4X}\right) \times 100 = \left(\frac{0.04}{1.4}\right) \times 100 = \frac{4}{14} \times 100 = \frac{200}{7} \approx 28.57\% \]

### Final Answer
The percentage earning of SBI at the end of two years on the entire amount is approximately **28.57%**.