Automobile dealers are increasingly advertising the leasing of vehicles in lieu

of purchasing. In one case, a $$20,000$ automobile can be leased for $$375$ per

month for $36$ months, after which it is returned to the dealer. If the automobile

is purchased, it could be financed for $3$ years at a $10\%$ annual rate with a

down payment of $5\%$ and $36$ equal monthly payments. If at the end of the $36-$

month period the vehicle is estimated to be worth $$8,000,$ which would be the

preferred alternative? Assume that the time value of money to the buyer is

also $10\%$ per annum for this scenario.

Answer $$ it is cheaper to lease. The present value of the lease is $$11,628,$

and the present value of the purchase is $$14,065$