Math (midterm)

PV = $3

FV = $4

No. of weeks t = 1

FV = PV (1+r)^t

4 = 3 (1 + r)^1

1 + r = 1.3333

R = 0.3333 = 33.33%

Weekly APR = 33.33%

APR per year = 33.33% x 52 = 1,733.33%

EAR = [1 + (APR / m)]m – 1

EAR = [1 + 0.3333]52 – 1 = 3,139,165.16%

Find the PV of both options, compare them.

we are purchasing the car

the lowest PV is the best option.

PV = the PV of the lease payments, plus the $99

The interest rate for the leasing option = same as the interest rate of the loan

The PV of leasing is PV = $99 + $499{1 – [1 / (1 + 0.06/12)12(3)]} / (0.06/12) = $16,501.64

The PV of purchasing the car is the current price of the car minus the PV of the resale price. The PV of the resale price is:

PV = $23,000 / [1 + (0.06/12)]12(3) = $19,219.83

The PV of the decision to purchase is:

$35,000 – 19,219.83 = $15,780.17

In this case, it is cheaper to buy the car than lease it since the PV of the buying cash flows is lower.

break-even resale price

find the resale price that makes the PV of the two options the same

$35,000 – PV of Resale price = $16,501.64

PV of resale price = $18,498.36

Therefore - resale price that would make the PV of the lease vs buy decision is the FV of this value, so:

Breakeven resale price = $18,498.36 [1 + (0.06/12)]12(3) = $22,136.63