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 pays to Arun and the compound interest he earns from Akshay. Finally, we will determine Rohit's profit from the transaction.

### Step 1: Calculate Simple Interest (SI) that Rohit pays to Arun
The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( P = 86,000 \) (Principal amount)
- \( R = 5\% \) (Rate of interest)
- \( T = 2 \) years (Time period)

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

### Step 2: Calculate Total Amount Paid to Arun
The total amount Rohit pays to Arun after 2 years is:
\[ \text{Total Amount} = P + SI = 86000 + 8600 = 94600 \]

### Step 3: Calculate Compound Interest (CI) that Rohit earns from Akshay
The formula for Compound Interest is:
\[ CI = P \left(1 + \frac{R}{100}\right)^T - P \]
Where:
- \( P = 86,000 \) (Principal amount)
- \( R = 5\% \) (Rate of interest)
- \( T = 2 \) years (Time period)

Substituting the values:
\[ CI = 86000 \left(1 + \frac{5}{100}\right)^2 - 86000 \]
\[ = 86000 \left(1 + 0.05\right)^2 - 86000 \]
\[ = 86000 \left(1.05\right)^2 - 86000 \]
\[ = 86000 \times 1.1025 - 86000 \]
\[ = 94815 - 86000 = 8815 \]

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

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

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