Mr. X purchased a house from a company for ₹7,00,000 and made a down payment of ₹1,50,000. He repays the balance in 25 years by equal monthly installments at 9% per annum compounded monthly. The equated monthly installment (EMI) is: [Given that $(1.0075)^{-300} = 0.106$]
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → ₹4614
Principal to be financed: $P = 700000 - 150000 = 550000$
Monthly interest rate: $i = \frac{9\%}{12} = 0.0075$
Number of monthly installments: $n = 25 \times 12 = 300$
EMI formula:
$EMI = P \cdot \frac{i}{1 - (1 + i)^{-n}}$
Substitute values:
$EMI = 550000 \cdot \frac{0.0075}{1 - (1.0075)^{-300}}$
Given: $(1.0075)^{-300} = 0.106$
$EMI = 550000 \cdot \frac{0.0075}{1 - 0.106} = 550000 \cdot \frac{0.0075}{0.894}$
$EMI = 550000 \cdot 0.00839 \approx 4614.5$