Harppreet borrowed Rs 20000 from her friend at 12% per annum simple interest. She lent it to Alam at the same rate but compounded annually. Find her gain after 2 years.

Answer

To solve the problem step by step, we will calculate the simple interest, the compound interest, and then find the gain Harpreet made after lending the money.

### Step 1: Calculate Simple Interest (SI)
The formula for simple interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( P = 20000 \) (Principal)
- \( R = 12 \) (Rate of interest per annum)
- \( T = 2 \) (Time in years)

Substituting the values:
\[ SI = \frac{20000 \times 12 \times 2}{100} \]

Calculating:
\[ SI = \frac{480000}{100} = 4800 \]

### Step 2: Calculate Amount for Compound Interest (A)
The formula for the amount when compounded annually is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
Substituting the values:
\[ A = 20000 \left(1 + \frac{12}{100}\right)^2 \]

Calculating:
\[ A = 20000 \left(1 + 0.12\right)^2 = 20000 \left(1.12\right)^2 \]
\[ A = 20000 \times 1.2544 = 25088 \]

### Step 3: Calculate Compound Interest (CI)
The formula for compound interest is:
\[ CI = A - P \]
Substituting the values:
\[ CI = 25088 - 20000 \]
Calculating:
\[ CI = 5088 \]

### Step 4: Calculate Gain
The gain is the difference between the compound interest earned and the simple interest paid:
\[ \text{Gain} = CI - SI \]
Substituting the values:
\[ \text{Gain} = 5088 - 4800 \]
Calculating:
\[ \text{Gain} = 288 \]

### Final Answer
Harpreet's gain after 2 years is Rs 288.

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