Question

You have decided to buy a used car. The dealer has offered you two options: (EV of $1. PV of $1. EVA of $1, and PVA of $1) (Use the appropriate factor(s) from the tables provided.) a. 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%. b. 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? 1-a. Present value 1-b. Which offer is clearly a better deal?

Answer 1

1-a
Annual Interest = 24%, Monthly Interest = 24%/2 = 12%

PV = Monthly Payment x PV annuity for 20 periods + PV of last payment
PV annuity for 20 periods @ 2% = 16.35143, PV factor for 20th period @2% = 0.67297

PV = $530 x 16.35143 + $12000 x 0.67297 = $16741.90

1-b
One time payment of $15392 is clearly better deal, since it is lower than PV of other option

2.
Present value of Option 1 = $106000

PV factor @9% for 7 years = 5.03295
PV of Option 2 = $21000 x 5.03295 = $105691.95

3.
PV annuity for 10 years @ 8% = 6.71008, PV factor for 10th year @8% = 0.46319
PV = $200200 x 6.71008 + $2002000 x 0.46319 = $2270664.4