Question

In a recent advertisement a new car has a sale price of $32,000. The car company is giving you the option of receiving a $3500 cash rebate or a special interest rate (for those who qualify) at 0.9% for 5 years.

If the local bank will lend you the money at 4.5% for 5 years should you take the discount and borrow from the bank or select the low interest rate from the company?

What option would you select and how much would you save over the second option?

Answer 1

   For selecting the correct option we need to calculate the
   Future Value under both options.
  
a)   If discount is taken and borrow from Bank
  
   Given,
   Amount needed to be borrowed today
   =Present Value under this option
   = Sale Value of Car - Cash Rebate
   = $32000 - $3500
   = $28500
   Interest rate of Bank = r = 4.5% = 0.045
   No of years = n = 5 years
  
   So,
   Future Value of Amount borrowed today
   = Amount borrowed today * (1+r)n
   = $28500 * (1+0.045)5
   = $28500 * (1.045)5
   = $28500 * 1.24618
   = $35516
  
b)   If amount borrowed at low interest rate from the company
   Amount needed to be borrowed today
   =Present Value under this option
   = Sale Value of Car
   = $32000
   Interest rate of Bank = r = 0.9% = 0.009
   No of years = n = 5 years
  
   So,
   Future Value of Amount borrowed today
   = Amount borrowed today * (1+r)n
   = $32000 * (1+0.009)5
   = $32000 * (1.009)5
   = $32000 * 1.04582
   = $33466
  
   Therefore, Amount borrowed at low interest rate from company option
   should be selected as this resulted in lower future value than other option.
  
   Amount Saved = $35516 - $33466 = $2050