Question

Vibhuti bought a car worth ₹10,25,000 and made a down payment of ₹4,00,000. The balance is to be paid in 3 years by equal monthly installments at an interest rate of 12% p.a. The EMI that Vibhuti has to pay for the car is:
(Use $(1.01)^{-36} = 0.7$)

• A. ₹20,700.85
• B. ₹27,058.87
• C. ₹25,708.89
• D. ₹20,833.33

Answer 1

Answer: (D)

₹20,833.33

Answer 2

The formula for EMI is:
$EMI = P \cdot \frac{r(1 + r)^n}{(1 + r)^n - 1}$,
where:
$P$: Loan amount $= 6,25,000$,
$r$: Monthly interest rate $= \frac{12}{12}\% = 1\% = 0.01$,
$n$: Loan tenure in months $= 36$.
Substituting the values:
$EMI = 6,25,000 \cdot \frac{0.01(1 + 0.01)^{36}}{(1 + 0.01)^{36} - 1}$.
Given:
$(1.01)^{-36} = 0.7 \implies (1.01)^{36} = \frac{1}{0.7} = 1.4286$.
Simplify:
$EMI = 6,25,000 \cdot \frac{0.01 \cdot 1.4286}{1.4286 - 1}$.
Numerator:
$0.01 \cdot 1.4286 = 0.014286$.
Denominator:
$1.4286 - 1 = 0.4286$.
Simplify the fraction:
$\frac{0.014286}{0.4286} \approx 0.03333$.
Thus:
$EMI = 6,25,000 \cdot 0.03333 = 20,833.33$.
Final Answer:
20,833.33