A person has purchased a home for Rs. 10,00,000 with down payment of Rs. 2,00,000. He amortizes the balance at 9% per annum compounded monthly for 25 years. Then the equal monthly installment (EMI) is:

[Given that: $\frac{(1.0075)^{300} - 1}{(0.0075)(1.0075)^{300}} = 119.1616$]

Rs. 6713.57

The correct answer is Option (2) → Rs. 6713.57

Given:

Principal borrowed: $P = 10,00,000 - 2,00,000 = 8,00,000$

Rate of interest: $r = 9\%$ per annum compounded monthly → monthly rate $i = \frac{9}{12} \% = 0.0075$

Number of months: $n = 25*12 = 300$

EMI formula: $EMI = P \frac{i(1+i)^n}{(1+i)^n - 1}$

Compute $(1+i)^n = (1.0075)^{300}$

Approximation: $(1.0075)^{300} \approx e^{300*0.0075} = e^{2.25} \approx 9.4877$

EMI = $800000 \cdot \frac{0.0075 \cdot 9.4877}{9.4877 - 1} = 800000 \cdot \frac{0.07115775}{8.4877} \approx 800000 \cdot 0.008387 \approx 6709.6$

Answer: EMI ≈ Rs. 6,710