1. **Problem Statement:** Compare a car loan of 1200000 taken for 5 years and 7 years by calculating Monthly EMI, Principal amount, Total interest, and Total amount. 2. **Formula for EMI:** $$EMI = \frac{P \times r \times (1+r)^n}{(1+r)^n - 1}$$ where: - $P$ = Principal loan amount - $r$ = Monthly interest rate (annual rate divided by 12) - $n$ = Total number of monthly installments (loan tenure in months) 3. **Assumptions:** - Assume an annual interest rate of 10% (0.10) for calculation. - Monthly interest rate $r = \frac{0.10}{12} = 0.008333$. 4. **Calculations for 5 years (60 months):** - $n = 5 \times 12 = 60$ - Calculate EMI: $$EMI = \frac{1200000 \times 0.008333 \times (1+0.008333)^{60}}{(1+0.008333)^{60} - 1}$$ - Calculate $(1+0.008333)^{60} \approx 1.647$. - Numerator: $1200000 \times 0.008333 \times 1.647 = 16470$ - Denominator: $1.647 - 1 = 0.647$ - EMI $= \frac{16470}{0.647} \approx 25458$ - Total amount paid $= EMI \times n = 25458 \times 60 = 1527480$ - Total interest $= 1527480 - 1200000 = 327480$ 5. **Calculations for 7 years (84 months):** - $n = 7 \times 12 = 84$ - Calculate EMI: $$EMI = \frac{1200000 \times 0.008333 \times (1+0.008333)^{84}}{(1+0.008333)^{84} - 1}$$ - Calculate $(1+0.008333)^{84} \approx 1.983$ - Numerator: $1200000 \times 0.008333 \times 1.983 = 19830$ - Denominator: $1.983 - 1 = 0.983$ - EMI $= \frac{19830}{0.983} \approx 20172$ - Total amount paid $= EMI \times n = 20172 \times 84 = 1694448$ - Total interest $= 1694448 - 1200000 = 494448$ 6. **Summary Table:** | Tenure (Years) | Monthly EMI | Principal Amount | Total Interest | Total Amount | |----------------|-------------|------------------|----------------|--------------| | 5 | 25458 | 1200000 | 327480 | 1527480 | | 7 | 20172 | 1200000 | 494448 | 1694448 | **Explanation:** - Longer tenure reduces monthly EMI but increases total interest paid. - Shorter tenure increases EMI but reduces total interest. This helps you compare the financial impact of loan tenure on your car loan.