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)

Hint:

When calculating the EMI for different loan amounts, it's essential to use the EMI formula that factors in the loan amount, interest rate, and loan tenure. By breaking down the formula into smaller steps, such as calculating the monthly interest rate and converting the loan tenure into months, you can easily calculate the EMI for any given scenario. This method ensures that you can compare different loan options effectively based on their EMIs.

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).

Answer 2

The formula for EMI (Equated Monthly Installment) is:

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

Step 1: Define the given values:

Here: \[ r = \frac{\text{Annual Interest Rate}}{12} = \frac{6}{100 \cdot 12} = 0.005, \] \[ n = \text{Loan Tenure in Months} = 25 \times 12 = 300. \]

Step 2: Calculate the intermediate value:

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

Step 3: Calculate the EMI for each property:

For each property, we calculate the EMI by multiplying the loan amount by 0.0064.

Property P:

\[ \text{Loan Amount} = 45,00,000 - 5,00,000 = 40,00,000, \] \[ \text{EMI} = 40,00,000 \times 0.0064 = 25,600. \]

Property Q:

\[ \text{Loan Amount} = 55,00,000 - 5,00,000 = 50,00,000, \] \[ \text{EMI} = 50,00,000 \times 0.0064 = 32,000. \]

Property R:

\[ \text{Loan Amount} = 65,00,000 - 10,00,000 = 55,00,000, \] \[ \text{EMI} = 55,00,000 \times 0.0064 = 35,200. \]

Property S:

\[ \text{Loan Amount} = 75,00,000 - 15,00,000 = 60,00,000, \] \[ \text{EMI} = 60,00,000 \times 0.0064 = 38,400. \]

Step 4: Final Matching:

\[ (A) \, P \, (I) \, 25,600, \quad (B) \, Q \, (III) \, 32,000, \quad (C) \, R \, (IV) \, 35,200, \quad (D) \, S \, (II) \, 38,400. \]

Conclusion: Thus, the correct option is (2).