Many people lease their vehicle rather than buying it$.$ The main reason is to avoid

tying up so much of one$$s money in an automobile. You determine that you can buy a new vehicle for a total cost of $$20,000,$ or you can lease the same vehicle by paying $$5000$ down plus lease payments of $$400$ every month for $4$ years. At the end of the lease agreement, you return the car to the dealer and walk away.

If you buy the car, best estimates are that in $4$ years you will be able to sell it for

$$1,000.$ Ignoring all other factors, at what annual interest rate compounded monthly are these options equivalent?