Mr. X wishes to purchase a flat for Rs. 44,65,000 with a down payment of Rs. 10,00,000 and balance in equated monthly installments (EMI) for 25 years. If the bank charges 6% per annum compounded monthly, the EMI is:
[Given: \((1.005)^{300} = 4.4650\)]
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Rs. 22,325
The loan is the price minus the down payment, and interest is charged monthly:
\(P = 4465000 - 1000000 = 3465000\)
\(i = 6\% \div 12 = 0.5\% = 0.005 \text{ per month}\)
\(n = 25 \times 12 = 300\)
By the EMI formula (reducing balance method):
\( \displaystyle \text{EMI} = \frac{P\,i\,(1+i)^n}{(1+i)^n - 1} \)
\( \displaystyle = \frac{3465000 \times 0.005 \times 4.4650}{4.4650 - 1} \)
\( \displaystyle = \frac{3465000 \times 0.005 \times 4.4650}{3.4650} \)
Since \(3465000 \div 3.465 = 1000000\):
\(\text{EMI} = 1000000 \times 0.005 \times 4.465\)
\(= 5000 \times 4.465 = 22325\)
So the EMI is Rs. 22,325.