Question

A car company is offering a choice of deals. You can receive $2.000 cash back on the purchase, or a 37 percent APR. 4-year loan. The price of the car is $28,500 and you could obtain a 4-year loan from your credit union, at 8.7 percent APR. Since the cash back is used to reduce the size of the loan, the cost of the car is entirely paid for with the debt. Therefore, the true cost of each deal can be compared through the monthly payment. Compute the monthly payment of each deal. Which one is cheaper? 3.7 percent APR offer $2.000 cash back offer

Answer 1

EMI for 3.7 % APR offer is $ 639.68

EMI for $ 2,000 cash back offer $ 655.69

Hence 3.7 % offer is cheaper

Explanation:

Formula to compute EMI is:

EMI = [P x r x (1+r) ⁿ]/[(1+r) ⁿ – 1]

P = Principal of loan, r = Periodic rate

n = Number of periods = 4 years x 12 months = 48 periods

Computation of EMI for 3.7 % APR offer:

P = $ 28,500

r = Periodic rate = 3.7 % APR or 0.037/12 = 0.003083333333 p.m.

EMI = [$ 28,500 x 0.003083333333 x (1+0.003083333333) ⁴⁸]/ [(1+0.003083333333) ⁴⁸ – 1]

     = [$ 28,500 x 0.003083333333 x (1.003083333333) ⁴⁸]/ [(1.003083333333) ⁴⁸ – 1]

     = ($ 28,500 x 0.003083333333 x 1.15924890677594)/ (1.15924890677594– 1)

     = $ 101.868997671923/ 0.15924890677594

     = $ 639.684125525902 or $ 639.68

Computation of EMI for $ 2,000 cash back offer:

P = $ 28,500 - $ 2,000 = $ 26,500

r = Periodic rate = 8.7 % APR or 0.087/12 = 0.00725 p.m.

EMI = [$ 26,500 x 0.00725 x (1+ 0.00725) ⁴⁸]/ [(1+ 0.00725) ⁴⁸ – 1]

     = [$ 26,500 x 0.00725 x (1.00725) ⁴⁸]/ [(1.00725) ⁴⁸ – 1]

     = ($ 26,500 x 0.00725x 1.41445537680453)/ (1.41445537680453 – 1)

     = $ 271.752239268571/ 0.41445537680453

     = $ 655.68515810747 or $ 655.69