Answer:
It would be better to buy the car.
Nominal 26,446.81 (break even resale price)
Explanation:
We solve the present value of the salvage value at 6% APR
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity $28,000.0000
time 36.00
rate 0.00500
[tex]\frac{28000}{(1 + 0.005)^{36} } = PV[/tex]
PV 23,398.0577
Net present worth:
23,398.06 - 43,000 = 19,601.94
Lease option
PV of the monthly payment:
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 505.00
time 36
rate 0.005
[tex]505 \times \frac{1-(1+0.005)^{-36} }{0.005} = PV\\[/tex]
PV $16,599.8632
plus the 4,300 downpayment
present worth: -20.899,86
As the option from the purcahse gives a lower present worth it is preferable over the option to lease the vehicle
X - 43,000 = -20,899.86
X = 22,100.14
We have to look at which resale price the present value is equal to 22,100.14
[tex]PV \: (1+ r)^{time} = Nominal [/tex]
Principal 22,100.14
time 36.00
rate 0.00500
[tex]22100.14 \: (1+ 0.005)^{36} = Nominal [/tex]
Nominal 26,446.81
