To calculate Vibhuti's Equated Monthly Installment (EMI), the following formula is used:
\[ \text{EMI} = \frac{P \times r \times (1+r)^n}{(1+r)^n-1} \]
where:
- \( P \) denotes the Principal loan amount.
- \( r \) denotes the Monthly interest rate.
- \( n \) denotes the Number of installments.
Step 1: Determine the Principal Amount
The car's cost is ₹10,25,000, and a down payment of ₹4,00,000 was made. The principal loan amount is therefore:
\( P = 10,25,000 - 4,00,000 = 6,25,000 \)
Step 2: Calculate the Monthly Interest Rate
The annual interest rate is 12%. The monthly interest rate is calculated as:
\( r = \frac{12}{100 \times 12} = 0.01 \)
Step 3: Establish the Number of Installments
The loan is to be repaid over 3 years with monthly payments, resulting in:
\( n = 3 \times 12 = 36 \)
Step 4: Apply the EMI Formula
The calculated values are substituted into the EMI formula:
\[ \text{EMI} = \frac{6,25,000 \times 0.01 \times (1.01)^{36}}{(1.01)^{36}-1} \]
Given \( (1.01)^{-36} = 0.7 \), \( (1.01)^{36} \) is the reciprocal:
\( (1.01)^{36} = \frac{1}{0.7} \approx 1.4286 \)
\[ \text{EMI} = \frac{6,25,000 \times 0.01 \times 1.4286}{1.4286-1} \]
\[ = \frac{6,25,000 \times 0.01 \times 1.4286}{0.4286} \]
\[ = \frac{8,937.5}{0.4286} \approx 20,833.33 \]
Therefore, Vibhuti's EMI is ₹20,833.33.