Mr. X purchased a house from a company for Rs. 7,00,000 and made a down payment of Rs. 1,50,000. He repays the balance in 25 years by equal monthly installments at 9% per annum compounded monthly. The equated monthly installment (EMI) is:
[Given that \((1.0075)^{-300} = 0.106\)]
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Rs. 4614
The loan is the price minus the down payment; the monthly rate and the number of instalments follow from the data:
\(P = 700000 - 150000 = 550000\)
\( \displaystyle i = \frac{9}{12 \times 100} = 0.0075 \)
\(n = 25 \times 12 = 300\)
By the EMI formula (reducing balance method):
\( \displaystyle \text{EMI} = \frac{P\,i}{1 - (1+i)^{-n}} \)
\( \displaystyle = \frac{550000 \times 0.0075}{1 - 0.106} \)
\( \displaystyle = \frac{4125}{0.894} \)
\( \approx 4614.1 \)
So the EMI is about Rs. 4614.