Question

Mr. Sanjay borrowed Rs.10,00,000 from a bank to purchase a car on reducing balance payment for a period of 10 years. If bank charges interest at 9% per annum compounded monthly and EMI is Rs.12,658 to be paid by him. Then principal outstanding after payment of 12th EMI is: (Use \( (1.0075)^{12 = 1.0938 \))}

• A. \( Rs.9,54,898 \)
• B. \( Rs.9,35,405 \)
• C. \( Rs.8,87,410 \)
• D. \( Rs.9,39,486 \)

Hint:

The reducing balance method ensures interest is calculated only on the current outstanding principal.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The outstanding principal after \( n \) payments is the present value of the remaining \( (N - n) \) EMIs.

Step 2: Key Formula or Approach:
The formula for outstanding principal \( P_{out} \) is:
\[ P_{out} = P(1+r)^n - EMI \times \frac{(1+r)^n - 1}{r} \]
Where \( P = 10,00,000 \), \( r = \frac{0.09}{12} = 0.0075 \), \( n = 12 \), and \( EMI = 12,658 \).

Step 3: Detailed Explanation:
\[ P_{out} = 10,00,000(1.0075)^{12} - 12,658 \times \frac{(1.0075)^{12} - 1}{0.0075} \]
Given \( (1.0075)^{12} = 1.0938 \):
\[ P_{out} = 10,00,000(1.0938) - 12,658 \times \frac{1.0938 - 1}{0.0075} \]
\[ P_{out} = 10,93,800 - 12,658 \times \frac{0.0938}{0.0075} \]
\[ P_{out} = 10,93,800 - 12,658 \times 12.5066 \]
\[ P_{out} = 10,93,800 - 1,58,317 \approx 9,35,483 \]
(Rounding variations lead to option B).

Step 4: Final Answer:
The principal outstanding is approximately \( Rs.9,35,405 \).