Question

A car lease requires payments of $465 at the beginning of each month for 7 years. If the lease rate is 4.40% compounded monthly, what should be the selling price of the car if you can purchase the car at the end of the lease for $13,000.

Answer 1

Solution

Selling price of car=PV of lease payments+pv of purchse price of car in end

Present value of lease payments=lease payment*((1-(1/(1+r)^n))/r)*(1+r)

Where r=intrest rate per period=4.4/12=0.366667% monthly

n=number of periods=12*7=84

lease payment=$465

Present value of lease payments=465*((1-(1/(1+.00366667)^84))/.00366667)*(1+.00366667)

=33688.11

pv of purchse price of car in end= purchse price of car in end/(1+r)^n

=13000/(1+.00366667)^84

=9559.28

Thus selling price of car=33688.11+9559.28=43247.39

Thus selling price of car=$43247.39