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 Equated Monthly Installment (EMI) is:

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

Where:

\( r \) is the monthly interest rate, calculated as \( r = \frac{\text{Annual Interest Rate}}{12} \). Given an annual interest rate of 6%, \( r = \frac{6}{100 \times 12} = 0.005 \).

\( n \) is the loan tenure in months. For a tenure of 25 years, \( n = 25 \times 12 = 300 \) months.

The calculated factor \( \frac{(1.005)^{300} \cdot 0.005}{(1.005)^{300} - 1} \) is 0.0064.

The EMI for each property is determined by:

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

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:

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

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

Matching results:

(A) Property P corresponds to EMI 25,600 (I)

(B) Property Q corresponds to EMI 32,000 (III)

(C) Property R corresponds to EMI 35,200 (IV)

(D) Property S corresponds to EMI 38,400 (II)

The correct option is (2).