A man deposited ₹ 6000 in a bank at 5% simple interest. Another man deposited 5000 at 8% compound interest. After 2 years, the difference of their interests will be

Options

A. ₹ `230`
B. ₹ `232`
C. ₹ `600`
D. ₹ `832`

Answer

To solve the problem, we need to calculate the simple interest for the first man and the compound interest for the second man, and then find the difference between the two interests.

### Step-by-Step Solution

**Step 1: Calculate Simple Interest for the First Man**
- Principal (P) = ₹6000
- Rate of Interest (R) = 5% per annum
- Time (n) = 2 years

The formula for Simple Interest (SI) is:
\[ SI = \frac{P \times R \times n}{100} \]

Substituting the values:
\[ SI = \frac{6000 \times 5 \times 2}{100} \]
\[ SI = \frac{60000}{100} = ₹600 \]

**Step 2: Calculate Compound Interest for the Second Man**
- Principal (P) = ₹5000
- Rate of Interest (R) = 8% per annum
- Time (n) = 2 years

The formula for Compound Interest (CI) is:
\[ A = P \left(1 + \frac{R}{100}\right)^n \]
Where A is the amount after n years. The Compound Interest is given by:
\[ CI = A - P \]

First, calculate the amount (A):
\[ A = 5000 \left(1 + \frac{8}{100}\right)^2 \]
\[ A = 5000 \left(1 + 0.08\right)^2 \]
\[ A = 5000 \left(1.08\right)^2 \]
Calculating \(1.08^2\):
\[ 1.08^2 = 1.1664 \]
Now substituting back:
\[ A = 5000 \times 1.1664 = ₹5832 \]

Now, calculate the Compound Interest (CI):
\[ CI = A - P = 5832 - 5000 = ₹832 \]

**Step 3: Calculate the Difference in Interests**
Now, we find the difference between the Compound Interest and the Simple Interest:
\[ \text{Difference} = CI - SI = 832 - 600 = ₹232 \]

### Final Answer
The difference of their interests after 2 years is ₹232.

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