Question

You are deciding whether you want to buy or lease a car that is worth $13,000. Its residual value after 2 years is $8,000, and after 4 years only $4,500. Assume an interest rate of 4.5% compounded monthly. If you take out a 4-year lease, what will be the monthly lease payment?...If you take out a 2-year lease, what will be the monthly lease payment?

Answer 1

PV of Lease Payments = Today’s Worth of Car – PV of Residual Value

Therefore,

PV of Lease Payments (2 years) = 13000 – [8000/{(1+0.00375)^24}] = 13000 – 7312.68 = 5687.32

PV of Lease Payments (4 years) = 13000 – [4500/{(1+0.00375)^48}] = 13000 – 3759.98 = 9240.02

PV of Annuity = P*[1-{(1+i)^-n}]/i

Where, PV = 5687.32, i = Interest Rate = 0.00375, n = Number of Periods = 24

Therefore,

5687.32 = P*[1-{(1+0.00375)^-24}]/0.00375

21.32745 = P*0.0859

Therefore, Lease Payments (2 years ) = Annuity = P = 21.32745/0.0859 = $248.28

Where, PV = 9240.02, i = Interest Rate = 0.00375, n = Number of Periods = 48

Therefore,

9240.02 = P*[1-{(1+0.00375)^-48}]/0.00375

34.650075 = P*0.1644485

Therefore, Lease Payments (4 years ) = Annuity = P = 34.650075/0.1644485 = $210.7