A person wishes to purchase a house for ₹39,65,000 with a down payment of ₹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 $(1.005)^{300} = 4.465$]

₹22325

The correct answer is Option (1) → ₹22325

Cost of house $=3965000$

Down payment $=500000$

Loan amount

$P=3965000-500000=3465000$

Rate of interest per annum $=6\%$

Rate per month

$r=\frac{6}{12\times100}=0.005$

Time $=25$ years

Number of monthly installments

$n=25\times12=300$

EMI formula on reducing balance method

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

Substitute values

$\text{EMI}=3465000\frac{0.005(1.005)^{300}}{(1.005)^{300}-1}$

$(1.005)^{300}\approx4.47$

$\text{EMI}=3465000\frac{0.005\times4.47}{3.47}$

$\text{EMI}\approx3465000\times0.00644$

$\text{EMI}\approx22318$

The EMI is approximately ₹22,318 per month.