You have $5,000 down payment on a $20,000 car. The dealer offers you the following two options:
(a) paying the balance with end-of-month payments over the next five years at
?^(12) = 9%.
(b) a reduction of $1000 in the price of the car, the same down payment of $5,000, and bank financing of the balance after down payment, over 5 years with end-of- month payments at ?^(12) = 12%.
Which option is better and why? (DO NOT USE EXCEL)
Formula for EMI is:
EMI = [P x r x (1+r) n]/ [(1+r) n-1
P = Loan amount or principal
r = Interest rate per month
n = Number of monthly installments
Computation of EMI for option (a)
P = $ 20,000 - $ 5,000 = $ 15,000
r = 0.09/12 = 0.0075 p.m.
n = 5 years x 12 months = 60
EMI = [$ 15,000 x 0.0075 x (1+0.0075)60]/ [(1+0.0075)60- 1]
= [$ 15,000 x 0.0075 x (1.0075)60]/ [(1.0075)60- 1]
= ($ 15,000 x 0.0075 x 1.56568102694157)/ (1.56568102694157 – 1)
= ($ 15,000 x 0.0075 x 1.56568102694157)/0.56568102694157
= $ 176.139115530927/0.56568102694157
= $ 311.375328395307 or $ 311.38
Total payments = $ 311.38 x 60 = $ 18,682.80
Computation of EMI for option (b)
P = $ 20,000 - $ 5,000 - $ 1,000 = $ 14,000
r = 0.12/12 = 0.01 p.m.
n = 5 years x 12 months = 60
EMI = [$ 14,000 x 0.01 x (1+0.01)60]/ [(1+0.01)60- 1]
= [$ 14,000 x 0.01 x (1.01)60]/ [(1.01)60- 1]
= ($ 14,000 x 0.01 x 1.81669669856409)/ (1.81669669856409– 1)
= ($ 14,000 x 0.01 x 1.56568102694157)/0.81669669856409
= $ 254.337537798973/0.81669669856409
= $ 311.422267588625 or $ 311.42
Total payments = $ 311.42 x 60 = $ 18,685.20
Both options are almost same in term of EMI but total payment for option (a) is less than option (b)
Hence option (a) seems to be better.
You have $5,000 down payment on a $20,000 car. The dealer offers you the following two...
You have $5,000 down payment on a $20,000 car. The dealer offers you the following two options: (a) paying the balance with end-of-month payments over the next five years at % (b) a reduction of $1000 in the price of the car, the same down payment of $5,000, and bank financing of the balance after down payment, over 5 years with end-of-month payments at 12% Which option is better and why? 12_9 12
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