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 $(1.015)^{-360} = 0.0047$]

Rs. 1,50,000

The correct answer is Option (2) → Rs. 1,50,000 **

Principal $P = 99{,}53{,}000$

Annual interest rate = $18\%$ compounded monthly

Monthly rate = $\frac{18}{12}=1.5\% = 0.015$

Number of monthly instalments $n = 30\times 12 = 360$

EMI formula (reducing balance):

$\displaystyle \text{EMI}=P\cdot \frac{r(1+r)^n}{(1+r)^n - 1}$

Given $(1.015)^{-360}=0.0047$

$\Rightarrow (1.015)^{360}=\frac{1}{0.0047}\approx 212.77$

Substitute:

$\text{EMI}=9953000\cdot \frac{0.015(212.77)}{212.77 - 1}$

EMI:

$\displaystyle \text{EMI}=\frac{31767331.15}{211.77}\approx 150000$

Required EMI ≈ ₹1,50,000 per month