Question

Dean is planning to purchase a car for $28,560. He has 12% to put down and can finance the remainder for 5 years.   He can get a loan at 2.14% APR.

1. Since Dean has the down payment amount already, if he puts that in a money market savings account with the APR of 3.5% what amount would he have to deposit each month to have the full $28,560 cost of the car so he could pay cash for it in five years?   

                                                                                                                                                                      

2. If Dean saves up to pay cash for his car (as calculated in question #6) instead of financing it what will be the total that he has to deposit into the savings account to accumulate the cost of the car?  

  

3. How much less will Dean pay for the car if he saves up to pay cash for his car instead of financing it?

Answer 1

APR is 3.5%, so EAR(Effective Annual Return)= (1+3.5%/12)^12-1=3.557%, monthly rate=3.5%/12=0.2917%, tenure=5*12=60 months

He has $28560*12% or $3427.20 and if he deposit this money in savings account, the future at the end 5 year=3427.2*(1+0.2917%)^60=4081.68

To pay in cash he needs 28560-4081.56= $24478.44 at the end of 5 year.

So, he needs to deposit $372.82 at the begining of each month to buy the car in cash.

So, total deposit= cash in hand+total monthly payment= 3427.2+372.82*60=$25796.4

If he finance it, then monthly rate=2.14%/12=0.178%, nper=60, loan amount(pv)=28560*(1-12%)=25132.8

So, total amount he will pay= 3427.2+442.06*60=$29950.8

So, he will pay (29950.8-25796.4)=$4154.4 less if he pay in cash instead of financing.