12. (EAIR in loans) You\'re considering buying a new top-of-the-line luxury car.
ID: 2817014 • Letter: 1
Question
12. (EAIR in loans) You're considering buying a new top-of-the-line luxury car. The car's list price is $99,000. The dealer has offered you two alternatives for purchasing the car: .You can buy the car for $90,000 in cash and get a $9,000 discount in the bargain. You can buy the car for the list of $99,000. In this case, the dealer is willing to take $39,000 as an initial payment. The remainder of $60,000 is a “zero-interest loan" to be paid back in equal install- ments over 36 months. Alternatively, your local bank is willing to give you a car loan at an annual interest rate of 10%, compounded monthly (that is, 10%/12 per month). Decide how to finance the car: Bank loan or zero-interest loan with the dealer, or cash payment.Explanation / Answer
Option 1:
Bank Loan = $ 90000
In this case, let us assume that loan is repaid in 3 years.
EMI Per month
Loan Amount = EMI / (1+(0.10/12))^1 + EMI / (1+(0.10/12))^2 +.....+ EMI / (1+(0.10/12))^35+ EMI / (1+(0.10/12))^36
90000 = EMI / (1+(0.10/12))^1 + EMI / (1+(0.10/12))^2 +.....+ EMI / (1+(0.10/12))^35+ EMI / (1+(0.10/12))^36
Solving above equation we get
EMI = $ 2904 per month
Now future value of all EMI's at end of 3 years = 2904*(1+(0.1/12))^1 + 2904*(1+(0.1/12))^2 + .... + 2904*(1+(0.1/12))^36 = $122345
Option 2: zero interest loan
EMI = 60000/36 = 1667
Future value of all payments: 1667 *(1+(0.1/12))^1+1667 *(1+(0.1/12))^2+....+1667 *(1+(0.1/12))^36 + 39000 *(1+(0.1/12))^36
= 70230 + 52579 = $122809
Option 3: Cash Payment
Future Value of Cash payment = 90000*(1+0.10/12)^36 = $121336
Option 3 - Cash purchase is the best choice as it involves the minimum payment
PS: we can solve the above sum by comparing the present value of payments as well
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