A person deposited a sum of `Rs.6,000` in a bank at `5%` per annum simple interest. Another person deposited `Rs. 5,000` at `8%` per annum compound interest. After two years, the difference of their interests will be

Options

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

Answer

To solve the problem, we need to calculate the simple interest earned by the first person and the compound interest earned by the second person after two years. Then, we will find the difference between these two amounts.

### Step 1: Calculate Simple Interest for the First Person

The formula for Simple Interest (SI) is given by:

\[ SI = \frac{P \times R \times T}{100} \]

Where:
- \( P \) = Principal amount (Rs. 6000)
- \( R \) = Rate of interest (5%)
- \( T \) = Time (2 years)

Substituting the values into the formula:

\[ SI = \frac{6000 \times 5 \times 2}{100} \]

Calculating the above expression:

\[ SI = \frac{6000 \times 10}{100} = \frac{60000}{100} = 600 \]

So, the simple interest earned by the first person after 2 years is Rs. 600.

### Step 2: Calculate Compound Interest for the Second Person

The formula for Compound Interest (CI) is:

\[ A = P \left(1 + \frac{R}{100}\right)^T \]

Where:
- \( A \) = Amount after time \( T \)
- \( P \) = Principal amount (Rs. 5000)
- \( R \) = Rate of interest (8%)
- \( T \) = Time (2 years)

First, we calculate the amount \( A \):

\[ A = 5000 \left(1 + \frac{8}{100}\right)^2 \]

Calculating \( \frac{8}{100} \):

\[ A = 5000 \left(1 + 0.08\right)^2 = 5000 \left(1.08\right)^2 \]

Calculating \( (1.08)^2 \):

\[ (1.08)^2 = 1.1664 \]

Now substituting back:

\[ A = 5000 \times 1.1664 = 5832 \]

Now, we find the compound interest \( CI \):

\[ CI = A - P = 5832 - 5000 = 832 \]

So, the compound interest earned by the second person after 2 years is Rs. 832.

### Step 3: Calculate the Difference in Interests

Now, we find the difference between the compound interest and the simple interest:

\[ \text{Difference} = CI - SI = 832 - 600 = 232 \]

Thus, the difference of their interests after two years is Rs. 232.

### Final Answer:
The difference of their interests after two years is Rs. 232.

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