Question

Buying the Car Now → Present Value Today or Payment Plan? A local car dealer has a used car that would suit Akash. The dealer is offering monthly payments of $300 for 2 years. The payment plan already includes interest at 9% per annum, compounded monthly.

1. How much will Akash pay in total if he decides to use the payment plan of $300 per month for 2 years?

2. How much will he pay for the car if he pays the present value today? Remember that the present value is the amount without interest.

3. How much less will he pay if he pays the present value today instead of accepting the payment plan?

4. Why might Akash prefer the payment plan even though it will cost him more overall? Make reference to the above calculations.

5. Why might it be better for Akash to save regularly for 4 years to buy a car, instead of buying this one now? Make reference to the above calculations.

Answer 1

1.

if he decides to use the payment plan of $300 per month for 2 years over all amount to be paid in 2 years=

=$300 Permonth * 12 month per year * 2 year

=$7200

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2.

PV = FV/ (1+ r)^n

where PV= present value

FV= future value

r= rate per period

n=Total period

PV of an annuity payment = A * (PVF , r, 0-n )

A= payment per period

(PVF, r,0-n period) = Cumulative PVF for n perids @r%

Here rate per month = 9%/12 = 0.75%

If he decided to pay the present value of the car today, then amount to be paid today=

= $300 * ( PVF , 0.75%, 24 months)    = $300* 18.51 = $5553

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3.

Less amount he will pay if he pays the present value today instead of accepting the payment plan=

=$7200- $ 5553 = $1647

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4.

Even if the over all cost in case of payment plan is more than the cost under present value plan , akash may choose to pay under monthly payment plan if Interest on investment or savings is more than 9% per annum.

Because Akash can invest the the Present value today and earn interest say 10% and can use the money to pay moonthly $300 including 9% interest.

In such case theere will be 1% savings in the interest.

-For example present value as calculated in point 2, is $ 5553. Now Akash will invest such amount @10% Per annum. After one month the interest income will be $46.275 ( $5553*10%*1/12) and nterest expenses monthly will be $41.6475 ( $5553*9%*1/12).

-There will be net saving of $46.275 - $41.6475 = $4.6275.

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5.

It is better to save regularly and buy a new car instead of buying a used car today.

- Because if he is buying now then he will have to pay interest element @9% . But in case of savings Mr. Akash will earn the interest on the savings and can use the savings plus the interest to buy a new car.

-New cas has more efficient than th eold used car.

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