Rohit borrows Rs 86,000 from Arun for two years at 5% per annum simple interest. He immediately lends out this money to Akshay at 5% compound interest compounded annually for the same period. Calculate Rohit's profit in the transaction at the end of two years.

Answer

To solve the problem step-by-step, we will calculate the simple interest Rohit has to pay to Arun and the compound interest he earns from Akshay. Finally, we will find Rohit's profit from the transaction.

### Step 1: Calculate the Simple Interest Rohit has to pay to Arun
The formula for Simple Interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \(P = 86000\) (Principal amount borrowed)
- \(R = 5\%\) (Rate of interest)
- \(T = 2\) years (Time period)

Substituting the values into the formula:
\[ SI = \frac{86000 \times 5 \times 2}{100} \]
Calculating the values:
\[ SI = \frac{86000 \times 10}{100} = \frac{860000}{100} = 8600 \]

### Step 2: Calculate the Compound Interest Rohit earns from Akshay
The formula for the Amount (A) in Compound Interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
Where:
- \(P = 86000\) (Principal amount lent)
- \(R = 5\%\) (Rate of interest)
- \(T = 2\) years (Time period)

Substituting the values into the formula:
\[ A = 86000 \left(1 + \frac{5}{100}\right)^2 \]
Calculating:
\[ A = 86000 \left(1 + 0.05\right)^2 = 86000 \left(1.05\right)^2 = 86000 \times 1.1025 \]
Calculating the amount:
\[ A = 86000 \times 1.1025 = 94815 \]

### Step 3: Calculate the Compound Interest earned
The Compound Interest (CI) is given by:
\[ CI = A - P \]
Substituting the values:
\[ CI = 94815 - 86000 = 8815 \]

### Step 4: Calculate Rohit's Profit
Rohit's profit is the difference between the compound interest earned and the simple interest paid:
\[ \text{Profit} = CI - SI \]
Substituting the values:
\[ \text{Profit} = 8815 - 8600 = 215 \]

### Final Answer
Rohit's profit in the transaction at the end of two years is **Rs 215**.

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