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]

The total house price is ₹7,00,000.

Down payment made is ₹1,50,000.

Loan amount (Principal):

$P = 7,00,000 - 1,50,000$

$P = 5,50,000$

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Time period is 25 years, which equals 300 months.

Annual interest rate is 9%.

Monthly interest rate:

$r = \dfrac{9\%}{12}$

$r = 0.75\%$

$r = 0.0075$

Number of payments: $n = 300$ months

Given: $(1.0075)^{-300} = 0.106$

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The EMI formula is:

$\text{EMI} = \dfrac{P \times r \times (1+r)^n}{(1+r)^n - 1}$

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To find $(1.0075)^{300}$:

$(1.0075)^{300} = \dfrac{1}{(1.0075)^{-300}}$

$(1.0075)^{300} = \dfrac{1}{0.106}$

$(1.0075)^{300} = 9.434$

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Substituting values into the EMI formula:

$\text{EMI} = \dfrac{5,50,000 \times 0.0075 \times 9.434}{9.434 - 1}$

Numerator:

$5,50,000 \times 0.0075 = 4,125$

$4,125 \times 9.434 = 38,915.25$

Denominator:

$9.434 - 1 = 8.434$

EMI:

$\text{EMI} = \dfrac{38,915.25}{8.434}$

$\text{EMI} = 4,614.45$

$\text{EMI} \approx ₹4,614$

Therefore, the equated monthly installment is ₹4,614.