A man plans to take a housing loan of Rs. 99,53,000 from a bank costing 18% per annum compounded monthly. The loan is to be paid back in 30 years in equal monthly installments (EMI). The EMI by reducing balance method is:
[Given \((1.015)^{-360} = 0.0047\)]
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Rs. 1,50,000
Monthly rate and number of instalments:
\( \displaystyle i = \frac{0.18}{12} = 0.015 \)
\( n = 30 \times 12 = 360 \)
By the reducing balance method, the loan P is the present value of the EMIs:
\( \displaystyle EMI = \frac{P\,i}{1 - (1+i)^{-n}} \)
\( \displaystyle = \frac{99{,}53{,}000 \times 0.015}{1 - 0.0047} \)
\( \displaystyle = \frac{1{,}49{,}295}{0.9953} \)
\( = 1{,}50{,}000 \)
So the EMI is Rs. 1,50,000.