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: .
Here, let the principal amount be the original balance to be paid before any interest, denoted as . The down payment is ₹7,50,000 which needs to be excluded from the calculation of interest on installment payments.
. Thus, the interest amount derived from monthly instalments of ₹22,000 over 10 years is .
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). .
Simplifying, .
.
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.