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 $530 per month for 20 months and an additional $12,000 at the end of 20 months. The dealer is charging an annual interest rate of 24%.
2. Make a one-time payment of $15,392, 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?

Present Value:

Which offer is clearly a better deal?:

Answer 1

1-a)

The dealer will charge $ 16,742.03 in option (a).

1-b)

PV of option (a) is $ 16,742.03

PV of option (b) is 15,392

In present value term, option (b), one-time payment while purchasing the car is a better deal.

Explanation:

Computation of PV of $ 530 annuity:

PV = P x PVIFA (i, n)

P = Periodic cash payment = $ 530

i = Periodic rate = 24 % p.a. or 24%/12 = 2 % p.m.

n = Number of payments = 20

PV = $ 530 x PVIFA (2 %, 20)

      = $ 530 x 16.351 = $ 8,666.03

PV of lump sum at the end of 20 payments:

PV = FV x PVIF (2 %, 20)

      = $ 12,000 x 0.6730 = $ 8,076

Total PV = $ 8,666.03 + $ 8,076 = $ 16,742.03