Question

You will buy a new car today.  You will borrow the full price of the car.  You will get a FIVE  year loan that will be paid back annually.  It will take you the full FIVE  years to pay back the loan.  (In other words, you will not pay it off early.)  You will pay back the same amount every year (an annuity). The auto dealership offers you 3 choices.

1)  Pay $30,000 for the car at 0% interest for the FIVE  years.   

2)  Pay $28,000 for the car at 2% interest for the FIVE  years.

3)  Pay $25,000 for the car at 4% interest for the FIVE  years.

Which do you pick?

Answer 1

Answer :

We will pick option 3 as our choice because total cost of the car is lowest out of the three choices .

Reason :

For this purpose we need to calculate the installment under each of the three alternatives

Calculation of Monthly installment in option 1

=PMT(rate,nper,pv)

where rate is the rate of interest per period i.e 0%

nper is thenumber of payments i.e 5

pv is the loan amount i.e 30000

=PMT(0%,5,-30000)

The loan installment is 6000 every year

Total Payment to be made in five years is 6000 * 5 = 30,000

Calculation of Monthly installment in option 2

=PMT(rate,nper,pv)

where rate is the rate of interest per period i.e 2%

nper is thenumber of payments i.e 5

pv is the loan amount i.e 28000

=PMT(2%,5,-28000)

The loan installment is 5940.44 every year

Total Payment to be made in five years is 5940.44 * 5 = 29702.18

Calculation of Monthly installment in option 3

=PMT(rate,nper,pv)

where rate is the rate of interest per period i.e 4%

nper is thenumber of payments i.e 5

pv is the loan amount i.e 25000

=PMT(4%,5,-25000)

The loan installment is 5615.68 every year

Total Payment to be made in five years is 5615.68 * 5 = 28078.39

Therefore least is in case of option 3 therefore select option 3.