Question

You have decided to buy a used car. The dealer has offered you two options: (FV of $1, PV of $1, FVA of $1, and PVA of $1) (Use the appropriate factor(s) from the tables provided.) Pay $550 per month for 30 months and an additional $12,000 at the end of 30 months. The dealer is charging an annual interest rate of 24%. Make a one-time payment of $17,593, due when you purchase the car. 1-a. Determine how much cash the dealer would charge in option (a). (Round your answer to 2 decimal places.)

WHAT IS THE PRESENT VALUE?

Answer 1

Determination of cash dealer would charge in option (a):

Present value of the monthly payment   $12,318
[$550 x 22.3965 Present value annuity factor (2%,30 months)]  
Present value of additional payment   $6,625
[$12,000 x 0.55207 Present value factor (2%,30 months )]  
Total   $18,943
Note: Given that annual interest rate is 24%.So that monthly interest is 2% (24%/12)

Present value factors taken from 'Present value tables'

Requirement b:

In present value terms,

Make a One-time payment of $17,593 is better because it is lower than the Option (a) which is $18,943.