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.)

1. Pay $570 per month for 25 months and an additional $12,000 at the end of 25 months. The dealer is charging an annual interest rate of 24%.
2. Make a one-time payment of $17,093, 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.)

1-b. In present value terms, which offer is clearly a better deal?

Answer 1

Answer 1-a:

Option 1:

Monthly Payment = $570
Lump Sum Payment = $12,000
Number of Payment = 25

Annual Interest Rate = 24%
Monthly Interest Rate = 24% / 12
Monthly Interest Rate = 2%

Present Value = $570 * PVA of $1 (2%, 25) + $12,000 * PV of $1 (2%, 25)
Present Value = $570 * 19.523 + $12,000 * 0.610
Present Value = $18,448.11

Option 2:
Lumpsum payment today = $17,093

Answer 1-b:

In present value terms, Option 1 is better as its present value is higher than present value of Option 2.