Question

A property dealer wishes to buy different houses given in the table below with some down payments and balance in EMI for 25 years. Bank charges 6% per annum compounded monthly.

• (A) - (I), (B) - (II), (C) - (III), (D) - (IV)
• (A) - (I), (B) - (III), (C) - (IV), (D) - (II)
• (A) - (III), (B) - (IV), (C) - (I), (D) - (II)
• (A) - (III), (B) - (IV), (C) - (II), (D) - (I)

Answer 1

The Correct Option is B

The formula for EMI is:

\( \text{EMI} = \text{Loan Amount} \times \frac{(1 + r)^n \cdot r}{(1 + r)^n - 1} \).

Here:

\( r = \frac{\text{Annual Interest Rate}}{12} = \frac{6}{100 \cdot 12} = 0.005 \),

\( n = \text{Loan Tenure in Months} = 25 \times 12 = 300 \),

The given value \( \frac{(1.005)^{300} \cdot 0.005}{(1.005)^{300} - 1} = 0.0064 \).

The EMI for each property is calculated as:

\( \text{EMI} = \text{Loan Amount} \times 0.0064 \).

For Property P:

\( \text{Loan Amount} = 45,00,000 - 5,00,000 = 40,00,000 \)

\( \text{EMI} = 40,00,000 \times 0.0064 = 25,600 \)

For Property Q:

\( \text{Loan Amount} = 55,00,000 - 5,00,000 = 50,00,000 \)

\( \text{EMI} = 50,00,000 \times 0.0064 = 32,000 \)

For Property R:

\( \text{Loan Amount} = 65,00,000 - 10,00,000 = 55,00,000 \)

\( \text{EMI} = 55,00,000 \times 0.0064 = 35,200 \)

For Property S:

\( \text{Loan Amount} = 75,00,000 - 15,00,000 = 60,00,000 \)

\( \text{EMI} = 60,00,000 \times 0.0064 = 38,400 \)

Final Matching: (A) P (I) 25,600 (B) Q (III) 32,000 (C) R (IV) 35,200 (D) S (II) 38,400

Thus, the correct option is (2).