A person wishes to purchase a house for Rs. 39,65,000 with a down payment of Rs. 5,00,000 and balance in equal monthly installments (EMI) for 25 years. If bank charges 6% per annum compounded monthly, then EMI on reducing balance payment method is:
[Given \((1.005)^{300} = 4.465\)]
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Rs. 22325
The loan is the cost minus the down payment, and the monthly rate and number of instalments follow from the data:
\(P = 3965000 - 500000 = 3465000\)
\( \displaystyle i = \frac{6}{12 \times 100} = 0.005 \)
\(n = 25 \times 12 = 300\)
By the EMI formula for the reducing balance method:
\( \displaystyle \text{EMI} = \frac{P\,i\,(1+i)^n}{(1+i)^n - 1} \)
\( \displaystyle = \frac{3465000 \times 0.005 \times 4.465}{4.465 - 1} \)
\( \displaystyle = \frac{3465000 \times 0.005 \times 4.465}{3.465} \)
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. 22325.