Question

You have decided to buy a used car. The dealer has offered you two options: (FV of S1, PV of $1, FVA of $1, and PVA of $1) (Use the appropriate factor(s) from the tables provided.)

a. Pay $540 per month for 25 months and an additional $10,000 at the end of 25 months. The dealer is charging an annual interest rate of 24%.
b. Make a one-time payment of $16,638, due when you purchase the car.
1-a. Determine how much cash the dealer would charge in option (a). (Round your final answer to nearest whole dollar.) Present value
1-b. In present value terms, which offer is clearly a better deal?
a. Option a
b. Option b
c. The present values of the options are nearly the same

Answer 1

1-a.

in order to determine the present value of option a we can look for the PVIFA (annuity factor) for 24% / 12 = 2% monthly rate and 25 payments.

PVIFA = 19.523

Present value of the 25 payments = $540 x 19.523 = $10,542.42

+

Present value of final payment = $10,000 / (1 + 24%)²⁵/¹² = $6,388.10

PV = $16,930.52

Present value of option b = $16,638

1-b.

• b. option b (lower present value)