Question

A person wishes to purchase a house for Rupess 39,65,000 with a down payment of Rupees 5,00,000 and balance in equal monthly installments (EMI) for 25 years. If bank charges 6% per annum compounded monthly, then EMI on reducing balance payment method is:
[Given \((1.005)^{300} = 4.465\)]

• A. Rupees 22325
• B. Rupees 36542
• C. Rupees 21652
• D. Rupees 34500

Hint:

When an exam question provides a calculated value like \((1.005)^{300} = 4.465\), it's a strong hint that you are on the right track and should use this value directly in your formula. This saves you from performing complex exponentiation.

Answer 1

The Correct Option is A

Step 1: Concept Identification:
The task is to compute the Equated Monthly Installment (EMI) for a loan using the reducing balance method, where interest is applied monthly to the outstanding principal.

Step 2: Core Formula:
The EMI calculation formula is:
\[ EMI = P \times r \times \frac{(1+r)^n}{(1+r)^n - 1} \]
Variables are defined as:
- \(P\) = Principal loan amount
- \(r\) = Monthly interest rate
- \(n\) = Total number of monthly installments

Step 3: Calculation Breakdown:
1. Principal Loan Amount (P): Calculated as Total House Cost minus Down Payment.
\[ P = 39,65,000 - 5,00,000 = 34,65,000 \]
2. Monthly Interest Rate (r): Derived from the annual rate of 6% compounded monthly.
\[ r = \frac{6\%}{12} = 0.5\% = 0.005 \]
3. Number of Installments (n): Determined by the loan term of 25 years.
\[ n = 25 \text{ years} \times 12 \text{ months/year} = 300 \text{ months} \]
4. EMI Calculation: Using the given value \((1+r)^n = (1.005)^{300} = 4.465\), substitute into the EMI formula.
\[ EMI = 34,65,000 \times 0.005 \times \frac{(1.005)^{300}}{(1.005)^{300} - 1} \]
\[ EMI = 17,325 \times \frac{4.465}{4.465 - 1} \]
\[ EMI = 17,325 \times \frac{4.465}{3.465} \]
\[ EMI \approx 17,325 \times 1.2886002886 \]
\[ EMI \approx 22324.59 \]

Step 4: Conclusive Result:
The EMI, rounded to the nearest rupee, is Rupees 22,325.