Question

Assume that you've been shopping for a new car and intend to finance part of it through an installment loan. The car you're looking for has a sticker price of $15,000. The local dealership has offered to sell it to you for $2,500 down and finance the balance with a loan that will require 48 monthly payments of $323.07; Adventure Vehicles will sell you the exact same vehicle for $2,000 down plus a 60-month loan for the balance, with monthly payments of $289.18. Which of these two finance packages is the better deal?

Answer 1

i ) first case Total value of car =$ 15000

Initial spot payment= $2500

Net loan Amount to pay further(PV of loan amount)= 15000-2500=$12500

Equated monthly Installment = $323.07

No of months EMI to be paid= 48

EMI= P*R(1+R)^N/(1+R)^N-1

323.07= 12500*R(1+R)⁴⁸ /(1+R)⁴⁸ -1

Suppose if we assume 1% interest the EMI will be 330 but actual EMI is 323.07 so it beneficial to the borrower/buyer from this case

ii) total amount for price= $15000

Initial payment = $ 2000

Loan Amount= $13000

EMI = 289.18 number of months =60

EMI=P*R(1+R)^N /(1+R)^N -1

289.18= 13000*R(1+R)^N /(1+R)^N -1

Suppose we assume interest rate is 1% the calculated EMI =289.18 Actual EMI is also 289.18 .

By comparing two cases first case actual EMI is less with calculated EMI by 1% interest .So we we can choose first case.