Mr. 'X' wishes to purchase a house for Rs. 49,65,000 with a down payment of Rs. 15,00,000 and balance amount in EMI for 25 years. If bank charges 6% per annum compounded monthly. Then the EMI is: [Given that \((1.005)^{300}= 4.4650\)]
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Rs. 22325
The loan is the price less the down payment:
\(P = 49{,}65{,}000 - 15{,}00{,}000 = 34{,}65{,}000\)
Interest is compounded monthly, so the rate per month and the number of months are
\( \displaystyle i = \frac{6}{12}\% = 0.5\% = 0.005,\quad n = 25 \times 12 = 300 \)
By the EMI formula (reducing balance method):
\( \displaystyle \text{EMI} = \frac{P\,i\,(1 + i)^n}{(1 + i)^n - 1} \)
\( \displaystyle \text{EMI} = \frac{3465000 \times 0.005 \times 4.4650}{4.4650 - 1} = \frac{17325 \times 4.4650}{3.4650} \)
Since \(17325 \div 3.4650 = 5000\):
\(\text{EMI} = 5000 \times 4.4650 = 22325\)
So the EMI is Rs. 22325.