Question

You need a new car and the dealer has offered you a price of $20,000​, with the following payment​ options: (a) pay cash and receive a $2,000 ​rebate, or​ (b) pay a $5,000 down payment and finance the rest with a 0% APR loan over 30 months. But having just quit your job and started an MBA​ program, you are in debt and you expect to be in debt for at least the next 2​ ½ years. You plan to use credit cards to pay your​ expenses; luckily you have one with a low​ (fixed) rate of 13.67% APR. Which payment option is best for​ you?

Answer 1

a)Pay Cash and receive $ 2000 a rebate

S.No	Particulars	Amount
A	Purchase price	$20,000
B	Rebate	$2,000
C	Net cost ( A-B)	$18,000

The payment under this system is $ 18000.

b) Given Down payment amount = $ 5000

Finance Amount = Purchase price - Down paymenst

= $ 20,000-$ 5000

= $ 15000

Since there is no interest , EMI for month is

EMI = Finance amount /No.of months

= $ 15000/30

= $ 500

Credit Card Rate of interest = 13.67% APR

Interest rate per month = 13.67% /12 = 1.139167%

We know that Present value of Ordinary Annuity = C [ {1-( 1+i)^-n}/i]

Here C = Cash flow per period

I = Interest rate per period

n = No.of payments

Present value of Payments = $ 500[ { 1-( 1+0.0113917)^-30}/0.0113917]

= $ 500[ { 1-( 1.0113917)^-30} /0.0113917]

= $ 500[ { 1-0.711899} /0.0113917]

= $ 500[ 0.288101/0.0113917]

= $ 500*25.29042

= $ 12645.21

Total payment under this method = Down payment + PV of the future payments

= $ 5000+$ 12645.21

= $17645.21

The present value of payment under option a ) is $ 18000 whereas under option b ) is $ 17645.21

Since the payment is lower in b ) option it is better to use credit card instead of availing Rebate.

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