Mr. Sharma lends Rs. 24,000 at 13% p.a. simple interest and an equal sum at 12% p.a. compound interest. Find the total interest earned by Mr. Sharma in 2 years.

Answer

To solve the problem, we need to calculate the simple interest earned by Mr. Sharma on Rs. 24,000 at 13% per annum for 2 years, and the compound interest earned on the same principal at 12% per annum for 2 years. Finally, we will sum these two interests to find the total interest earned.

### Step-by-Step Solution:

**Step 1: Calculate Simple Interest (SI)**
The formula for simple interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \(P\) = Principal amount = Rs. 24,000
- \(R\) = Rate of interest = 13% per annum
- \(T\) = Time period = 2 years

Substituting the values:
\[ SI = \frac{24000 \times 13 \times 2}{100} \]

**Step 2: Simplify the Simple Interest Calculation**
Calculating the above expression:
\[ SI = \frac{24000 \times 26}{100} = \frac{624000}{100} = 6240 \]
So, the simple interest earned is Rs. 6,240.

**Step 3: Calculate Compound Interest (CI)**
The formula for compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
Where:
- \(A\) = Amount after time \(T\)
- \(P\) = Principal amount = Rs. 24,000
- \(R\) = Rate of interest = 12% per annum
- \(T\) = Time period = 2 years

Substituting the values:
\[ A = 24000 \left(1 + \frac{12}{100}\right)^2 \]
\[ A = 24000 \left(1 + 0.12\right)^2 = 24000 \left(1.12\right)^2 \]

**Step 4: Calculate the Amount**
Calculating \( (1.12)^2 \):
\[ (1.12)^2 = 1.2544 \]
Now substituting back:
\[ A = 24000 \times 1.2544 = 30105.6 \]

**Step 5: Calculate Compound Interest**
Now, we find the compound interest:
\[ CI = A - P = 30105.6 - 24000 = 6105.6 \]
So, the compound interest earned is Rs. 6,105.6.

**Step 6: Calculate Total Interest**
Finally, we sum the simple interest and compound interest:
\[ \text{Total Interest} = SI + CI = 6240 + 6105.6 = 12345.6 \]

### Final Answer:
The total interest earned by Mr. Sharma in 2 years is Rs. 12,345.6.

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