Rakshita plans to buy a house for Rs.1,00,00,000 with down payment of 20% of the value of house paid by her mother, rest of the amount she wishes to pay in 25 years by equal monthly installment at an interest of 9% per annum compounded monthly. Then the EMI paid by her is: (Given \((1.0075)^{300} = 9\))
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Rs. 67,500
The loan is the price less the down payment:
\(P = 10000000 - 20\% \text{ of } 10000000 = 8000000\)
The monthly rate and the number of instalments are
\( \displaystyle i = \frac{9}{12 \times 100} = 0.0075 \)
\(n = 25 \times 12 = 300\)
By the EMI formula (reducing balance):
\( \displaystyle \text{EMI} = \frac{P\,i\,(1+i)^n}{(1+i)^n - 1} \)
\( \displaystyle = \frac{8000000 \times 0.0075 \times 9}{9 - 1} \)
\( \displaystyle = \frac{540000}{8} = 67500 \)
So the EMI is Rs. 67,500.