Mr. X wishes to purchase a house for Rs. 14,51,400 from a bank and decided to repay the loan by equal monthly installments (EMI) in 10 years. If bank charges interest at 9 % per annum compounded monthly, then the EMI is:
[Given that \((1.0075)^{120}=2.4514\)]
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Rs. 18385.50
By the reducing balance method, the EMI on a loan P at rate i per month for n months is
\( \displaystyle \text{EMI} = \frac{P\,i\,(1+i)^n}{(1+i)^n - 1} \)
Here
\(P = 1451400\)
\(i = \frac{9}{12 \times 100} = 0.0075\)
\(n = 10 \times 12 = 120\)
\( \displaystyle \text{EMI} = \frac{1451400 \times 0.0075 \times 2.4514}{2.4514 - 1} = \frac{1451400}{1.4514} \times 0.0075 \times 2.4514 \)
The loan has been chosen so that \(\frac{1451400}{1.4514} = 1000000\) exactly:
\(\text{EMI} = 1000000 \times 0.0075 \times 2.4514\)
\(= 7500 \times 2.4514 = 18385.50\)