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 $(1.005)^{300} = 4.465$]
Answer & explanation
Correct answer: option 1
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.