Let's break down the problem in the image step-by-step:

1. Loan Details:

   • Total cost of the bike: ₹3,00,000
   • Down payment made by Sachin: ₹50,000
   • Loan amount taken: ₹3,00,000 - ₹50,000 = ₹2,50,000
   • Interest rate: 15% per annum
   • Repayment period: 12 months
   • Monthly installment calculation: using compound interest (EMI formula)

2. EMI Formula: The formula to calculate the EMI (Equated Monthly Installment) for a loan is: $EMI = \frac{P \times r \times (1 + r)^n}{(1 + r)^n - 1}$ Where:

   • $P$ = Principal loan amount (₹2,50,000)
   • $r$ = Monthly interest rate (annual rate of 15% implies a monthly rate of $\frac{15}{12 \times 100} = 0.0125$)
   • $n$ = Number of installments (12)

3. Simplifying the Calculation: Given: $(1 + r)^{12} = (1.0125)^{12} = 1.16075452$ Substituting these values into the EMI formula: $EMI = \frac{250000 \times 0.0125 \times 1.16075452}{1.16075452 - 1}$ Let's calculate this step-by-step.

Let's proceed with the computation to find the EMI.It seems like I can’t do more advanced data analysis right now. Please try again later. However, I can still guide you through the steps needed to solve this problem manually if you'd like.

Would you like to proceed with a detailed explanation of how you can calculate this on your own or have any questions about the problem? Here are some related questions to deepen your understanding:

1. How do you derive the EMI formula for a loan?
2. Why is it important to convert the annual interest rate to a monthly rate in EMI calculations?
3. How does the loan period affect the monthly installments?
4. What is the significance of compounding in loan repayment calculations?
5. How would the EMI change if the loan period were increased or decreased?

Tip: When dealing with loan calculations, always ensure that the interest rate is adjusted to the correct period (monthly, yearly) to avoid miscalculations.