Mohan wishes to purchase a house for Rs. 10,000,000 with a down payment of Rs. 20,000,00. If he pays the balance amount in 25 years by equal monthly instalment at 9% compounded monthly, then the total interest paid by Mohan is:
[Use \( (1.0075)^{300}=9.4084 \)]
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Rs. 12,140,716
The down payment printed as Rs. 20,000,00 is Rs. 20,00,000 = Rs. 2,000,000, so the loan is
\( \displaystyle P=10{,}000{,}000-2{,}000{,}000=\text{Rs.}\ 8{,}000{,}000 \)
Monthly rate \( i=\frac{9}{12\times 100}=0.0075 \), number of instalments n = 25 × 12 = 300. The EMI on a reducing balance is
\( \displaystyle \text{EMI}=\frac{P\,i\,(1+i)^n}{(1+i)^n-1} \)
\( \displaystyle =\frac{8{,}000{,}000\times 0.0075\times 9.4084}{9.4084-1} \)
\( \displaystyle =\frac{60{,}000\times 9.4084}{8.4084} \)
\( \displaystyle =\frac{564{,}504}{8.4084} \)
\( \displaystyle \approx\text{Rs.}\ 67{,}135.72 \)
Total amount paid in instalments, and the total interest (total paid − loan):
\( \displaystyle 67{,}135.72\times 300=\text{Rs.}\ 20{,}140{,}716 \)
\( \displaystyle \text{Interest}=20{,}140{,}716-8{,}000{,}000=\text{Rs.}\ 12{,}140{,}716 \)
CBSE Applied Mathematics (Class XII):
Methods of Calculation of EMI or Instalment
