Question 754221: Can you please help me with this problem?
A car has a sticker price of $42,650 with factory and dealer rebates of $5,100.
You can pay the sticker price at 0% interest for 60 months.
You can pay the discount price at 2.5% add-on interest for 60 months.
a) Find the monthly payment if financed for 60 months at 0% APR. (Round to the nearest cent.)
b) Find the monthly payments if financed at 2.5% add-on interest for 60 months.
c)use the APR approximation formula to find the APR for part (b).
d? State whether the 0% APR or the 2.5% add-on rate should be preferred.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you can use an online calculator like the one shown below to do the add-on Interest Calculations.
http://www.csgnetwork.com/addonintcalc.html
you can use an online calculator like the one shown below to do the apr calculations.
http://www.carpaymentcalculator.net/
it makes a difference whether you are paying add-on interest on the original purchase price of the car or whether you are paying add-on interest on the discount price of the car and getting a check back from the dealer for the rebate.
we'll look at each scenario and see which one looks the best.
scenario 1 is financing the purchase price of $42,650 at 0% interest for 60 months.
using the apr calculator, you will find that the monthly payment is equal to $710.83
scenario 2 is financing the discount price of $37,550 at 2.5% add-on interest for 60 months.
using the add-on calculator, you will find that the monthly payment is equal to $704.06
scenario 3 is financing the purchase price of $42,650 at 2.5% add-on interest for 60 months and receiving a rebate check of $5,100 from the dealer.
using the add-on calculator, you will find that the monthly payment is equal to $799.69
the next question is which is cheaper for you?
you can compare scenario 1 to scenario 2, or you can compare scenario 1 to scenario 3.
let's look at scenario 1 compared to scenario 2 first.
scenario 1 costs you $710.83 per month for 60 months.
scenario 2 costs you $704.06 per month for 60 months.
you can compare these by taking the present value of the monthly payments at 2.5% interest rate.
the present value of $710.83 per month for 60 months at 2.5% apr is equal to $40136.16.
the present value of $704.06 per month for 60 months at 2.5% apr is equal to $39,753.90.
on a present value basis:
scenario 1 costs $40,136.16
scenario 2 costs $39,753.90
scenario 2 is the winner.
you have no cash in your pocket, but you are making less payments per month for the life of the loan.
let's look at scenario 1 compared to scenario 3 next.
scenario 1 costs you $710.83 per month
scenario 3 costs you $799.69 per month but you have $5,100 cash in your pocket.
the present value of 60 payments of $710.83 per month at 2.5% apr is equal to $40,136.16.
the present value of 60 payments of $799.69 per month at 2.5% apr is equal to $45,153.53.
take the $5,100 cash that you got back from the dealer and subtract it from $45,153.53 and you are left with $40,053.53
on a present value basis:
scenario 1 costs you $40,136.16
scenario 3 costs you $40,053.53
scenario 3 is the winner but they're extremely close.
it doesn't make much difference which one of these options you choose.
on a present value basis, they are roughly equivalent.
choose the one that fits your life style better.
do you want the reduced payments or do you want the cash?
in the long run, the net financial effect is the same.
this may or may not answer the question you posed.
i'm assuming you wanted to make a financial comparison.
to answer your questions directly, these would be the answers:
a) Find the monthly payment if financed for 60 months at 0% APR. (Round to the nearest cent.)
the monthly payment would be $710.83 per month.
b) Find the monthly payments if financed at 2.5% add-on interest for 60 months.
the monthly payments depend on whether the add-on interest payments are made on the original purchase price of the car or on the discount price of the car.
if made on the original purchase price, then the payments would be $799.69 per month.
if made on the discount price, then the payments would be $704.06 per month.
c)use the APR approximation formula to find the APR for part (b).
based on the original purchase price of $42,650, the equivalent apr would be:
if made on the original purchase price, then the equivalent apr would be 4.9%
if made on the discount price, then the equivalent apr would be -0.4%
d? State whether the 0% APR or the 2.5% add-on rate should be preferred.
the comparisons are very close and the apr comparisons doesn't really tell the whole story because it doesn't consider the cash back in scenario 3.
bottom line is that taking the discount gives you a better deal because you are either making smaller payments (scenario 1 versus scenario 2), or you are making larger payments but getting cash back up front (scenario 1 versus scenario 3).
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