Mr. Pawan invests an amount of X 24200 at the rate of 4% per annum for 6 yr to obtain a simple interest, later he invests the principal amount as well as the amount obtained as simple interest for another 4 yr at the same rate of interest. What amount of simple interest will be obtained at the end of the last 4 yr?

Options

A. X4800
B. X4850.32
C. X4801.30
D. X4702

Answer

To solve the problem step by step, we need to calculate the simple interest for the first 6 years and then use the total amount (principal + interest) to calculate the simple interest for the next 4 years.

### Step 1: Calculate the Simple Interest for the First 6 Years

The formula for Simple Interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
where:
- \( P \) = Principal amount (initial investment)
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

Given:
- \( P = 24200 \)
- \( R = 4\% \)
- \( T = 6 \)

Substituting the values into the formula:
\[ SI = \frac{24200 \times 4 \times 6}{100} \]

Calculating:
\[ SI = \frac{24200 \times 24}{100} \]
\[ SI = \frac{580800}{100} \]
\[ SI = 5808 \]

### Step 2: Calculate the Total Amount After 6 Years

Total Amount (A) after 6 years is given by:
\[ A = P + SI \]
Substituting the values:
\[ A = 24200 + 5808 \]
\[ A = 30008 \]

### Step 3: Calculate the Simple Interest for the Next 4 Years

Now, Mr. Pawan invests the total amount \( 30008 \) for another 4 years at the same rate of interest (4%).

Using the Simple Interest formula again:
\[ SI = \frac{P \times R \times T}{100} \]
where:
- \( P = 30008 \)
- \( R = 4\% \)
- \( T = 4 \)

Substituting the values:
\[ SI = \frac{30008 \times 4 \times 4}{100} \]

Calculating:
\[ SI = \frac{30008 \times 16}{100} \]
\[ SI = \frac{480128}{100} \]
\[ SI = 4801.28 \]

### Final Answer

The amount of simple interest obtained at the end of the last 4 years is **4801.28**.

---