Satyam took loan from IDIDI Bank for his 2 years course of MBA at IMD. He took the loan of ₹ 6 lakh such that he would be charged at `8%` per annum at CI during his course and at `10%` CI after the completion of course. He returned half of the amount which he had to be paid on the completion of his studies and remaining after 2 years What is the total amount returned by Satyam ?

Options

A. ₹ 7.73323 lakh
B. ₹ 7.58 lakh
C. ₹ 7.336 lakh
D. none of these

Answer

To solve the problem step by step, let's break it down:

### Step 1: Calculate the amount after 2 years at 8% Compound Interest (CI)

The formula for compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]
Where:
- \( A \) = Total amount after time \( n \)
- \( P \) = Principal amount (initial loan)
- \( r \) = Rate of interest per annum
- \( n \) = Number of years

Here, \( P = 6,00,000 \) (6 lakh), \( r = 8\% \), and \( n = 2 \).

Plugging in the values:
\[ A = 6,00,000 \left(1 + \frac{8}{100}\right)^2 \]
\[ A = 6,00,000 \left(1 + 0.08\right)^2 \]
\[ A = 6,00,000 \left(1.08\right)^2 \]
\[ A = 6,00,000 \times 1.1664 \]
\[ A = 6,99,840 \]

### Step 2: Calculate the amount after the course at 10% CI for the remaining amount

Satyam returns half of the total amount after the course. So, he pays:
\[ \text{Half of } A = \frac{6,99,840}{2} = 3,49,920 \]

The remaining amount after the first payment is:
\[ \text{Remaining amount} = 6,99,840 - 3,49,920 = 3,49,920 \]

Now, this remaining amount will accrue interest at 10% for 2 more years.

Using the compound interest formula again:
\[ A = 3,49,920 \left(1 + \frac{10}{100}\right)^2 \]
\[ A = 3,49,920 \left(1 + 0.10\right)^2 \]
\[ A = 3,49,920 \left(1.10\right)^2 \]
\[ A = 3,49,920 \times 1.21 \]
\[ A = 4,24,000.80 \]

### Step 3: Calculate the total amount returned by Satyam

Now, we add the amount he paid after the course and the amount he pays after 2 years:
\[ \text{Total amount returned} = 3,49,920 + 4,24,000.80 \]
\[ \text{Total amount returned} = 7,73,920.80 \]

### Final Answer
The total amount returned by Satyam is approximately ₹ 7,73,920.80.

---