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

The Correct Option is D

To find the EMI (Equated Monthly Installment) Vibhuti has to pay, we can use the formula for EMI:

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

where:

• \( P \) = Principal loan amount
• \( r \) = Monthly interest rate
• \( n \) = Number of installments

Step 1: Calculate the Principal Amount

The cost of the car is ₹10,25,000 and a down payment of ₹4,00,000 is made. Thus, the principal amount to be financed is:

\( P = 10,25,000 - 4,00,000 = 6,25,000 \)

Step 2: Convert Annual Interest Rate to Monthly

The annual interest rate is 12%. Hence, the monthly interest rate is:

\( r = \frac{12}{100 \times 12} = 0.01 \)

Step 3: Determine the Number of Installments

Since the balance is to be paid over 3 years with monthly installments:

\( n = 3 \times 12 = 36 \)

Step 4: Substitute in the EMI Formula

Substitute the values into the EMI formula:

\[ \text{EMI} = \frac{6,25,000 \times 0.01 \times (1.01)^{36}}{(1.01)^{36}-1} \]

Given \( (1.01)^{-36} = 0.7 \), we find \( (1.01)^{36} \) by taking reciprocal:

\( (1.01)^{36} = \frac{1}{0.7} \approx 1.4286 \)

\[ \text{EMI} = \frac{6,25,000 \times 0.01 \times 1.4286}{1.4286-1} \]

\[ = \frac{6,25,000 \times 0.01 \times 1.4286}{0.4286} \]

\[ = \frac{8,937.5}{0.4286} \approx 20,833.33 \]

Thus, the EMI Vibhuti has to pay is ₹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