A person has purchased a home for Rs. 10,00,000 with down payment of Rs. 2,00,000. He amortize the balance at 9% per annum compounded monthly for 25 years then the equal monthly installment (EMI) is:
[Given that: \(\displaystyle\frac{(1.0075)^{300} - 1}{(.0075)(1.0075)^{300}} = 119.1616\)]
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Rs. 6713.57
The loan is the balance after the down payment: Rs. 10,00,000 − Rs. 2,00,000 = Rs. 8,00,000.
\( \displaystyle i = \frac{9\%}{12} = 0.75\% = 0.0075 \text{ per month} \)
\(n = 25 \times 12 = 300 \text{ months}\)
Under the reducing balance method, the loan equals the present value of all the EMIs:
\( \displaystyle P = \text{EMI} \times \frac{(1 + i)^n - 1}{i\,(1 + i)^n} \)
\( \displaystyle 800000 = \text{EMI} \times \frac{(1.0075)^{300} - 1}{(0.0075)(1.0075)^{300}} \)
\(800000 = \text{EMI} \times 119.1616\)
\( \displaystyle \text{EMI} = \frac{800000}{119.1616} = 6713.57 \)
So the EMI is Rs. 6713.57.
CBSE Applied Mathematics (Class XII):
Methods of Calculation of EMI or Instalment
