Mr. X wishes to purchase a house for ₹ 14,51,400 from a bank and decided to repay the loan by equal monthly installments (EMI) in 10 years. If bank charges interest at 9 % per annum compounded monthly, then the EMI is:

[Given that $(1.0075)^{120} = 2.4514]$

Given:

Loan Amount (P) = ₹14,51,400

Time Period = 10 years = 120 months

Annual Interest Rate = 9%

Monthly Interest Rate (r) = $\frac{9\%}{12} = 0.75\% = 0.0075$

$(1.0075)^{120} = 2.4514$

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The EMI formula for loans with compound interest is:

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

where P is the principal, r is the monthly interest rate, and n is the number of months.

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Substituting the values:

$\text{EMI} = \frac{14,51,400 \times 0.0075 \times (1.0075)^{120}}{(1.0075)^{120} - 1}$

$\text{EMI} = \frac{14,51,400 \times 0.0075 \times 2.4514}{2.4514 - 1}$

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Calculating the numerator:

$14,51,400 \times 0.0075 = 10,885.5$

$10,885.5 \times 2.4514 = 26,680.31$

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Calculating the denominator:

$2.4514 - 1 = 1.4514$

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$\text{EMI} = \frac{26,680.31}{1.4514}$

$\text{EMI} = ₹18,385.50$

Therefore, the EMI is ₹18,385.50.