Question

A person buys a flat for which he makes down payment of ₹7,50,000 and the balance is to be paid in 10 years by monthly instalments of ₹22,000 each. If the bank charges interest at the rate of 12% per annum, then the actual price of the flat using flat rate system is:

• A. ₹20,50,000
• B. ₹19,50,000
• C. ₹22,00,000
• D. ₹18,50,000

Answer 1

The Correct Option is B

To determine the actual price of the flat using the flat rate system, we must first calculate the total payment including interest, then subtract the down payment.

Step 1: Compute the total amount of monthly instalments. Since each monthly installment is ₹22,000 and there are 12 months in a year over 10 years, the total number of payments is 10 × 12 = 120.

Total monthly instalments = ₹22,000 × 120 = ₹26,40,000.

Step 2: Calculate the total interest paid using the flat rate system. The flat rate interest for the entire tenure can be calculated using the formula for simple interest: \( \text{Interest} = \frac{\text{Principal} \times \text{Rate} \times \text{Time}}{100} \).

Here, let the principal amount be the original balance to be paid before any interest, denoted as \( x \). The down payment is ₹7,50,000 which needs to be excluded from the calculation of interest on installment payments.

\(\text{Total amount to be paid} = \frac{x \times 12 \times 10}{100} = \frac{120x}{100}\). Thus, the interest amount derived from monthly instalments of ₹22,000 over 10 years is \( \frac{120x}{100} = 0.12x \).

Step 3: Total amount paid (instalments + down payment) should account for both the principal and the interest, which equals to the ₹26,40,000 that includes principal ₹x and interest (0.12 x).\( x + 0.12x = ₹26,40,000 - ₹7,50,000 = ₹18,90,000 \).

Simplifying,\(1.12x = ₹18,90,000 \).

\(\therefore x = \frac{₹18,90,000}{1.12} \approx ₹16,87,500 \).

Step 4: Calculate actual price of the flat.
The total price equals down payment plus the principal on which interest is calculated: ₹7,50,000 + ₹16,87,500 = ₹19,37,500.

Thus, rounding accurately closest to the option choices available, the actual price of the flat using the flat rate system is ₹19,50,000.