Question

1. Suppose that you are debating whether to buy or lease a new Chevy Spark, which 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.

1a. If you take out a 4-year lease, what will be the monthly lease payment?

1b. If you take out a 2-year lease, what will be the monthly lease payment?

Answer 1

To get monthly payment we use formula

Payment = Present Value - (Future Value / ( ( 1 + i ) ^n) / [ 1- (1 / (1 +i ) ^ n ) ] / i.

Solution to 1a. $210.70

Where i =4.5/12 = 0.00375, FV=4500, PV = 13000, N=48

= { 13000 - (4500/((1+0.00375)^48)) } / (1-(1/(1+0.00375)^48))/0.00375

= $9240 / 43.85

= $210.70

Solution to 1b. $248.24

Explanation:

Where i =4.5/12 = 0.00375, FV=8000, PV = 13000, N=24

={ 13000- (8000/((1+0.00375)^24)) } / (1-(1/(1+0.00375)^24))/0.00375

= $5687.35/22.91

= $248.24