Sameer purchased a house worth Rs. 7,20,000 and made a down payment of Rs. 1,00,000. He repays the balance in 8 years by monthly instalments at 12% compounded monthly. His monthly instalment on reducing balance method is around : (use \( (1.01)^{-96}\approx 0.38 \))
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Rs. 10,000
The loan is the balance after the down payment, repaid by equal monthly instalments (EMI) on the reducing balance:
\( \displaystyle P=720000-100000=620000 \)
\( \displaystyle i=\frac{12\%}{12}=1\%=0.01\ \text{per month},\qquad n=8\times 12=96 \)
\( \displaystyle \text{EMI}=\frac{P\cdot i}{1-(1+i)^{-n}} \)
\( \displaystyle =\frac{620000\times 0.01}{1-(1.01)^{-96}} \)
\( \displaystyle =\frac{6200}{1-0.38} \)
\( \displaystyle =\frac{6200}{0.62}=10000 \)
So the monthly instalment is about Rs. 10,000.