leas or buy decision You are trying to decide whether to lease or buy an item for your project. The daily lease cost is $120. To purchase the item, the investme

Question

You ent cost is $1,000 and the daily maintenance cost is $20. How long will it take for the lease cost to be the same as the purchase cost? are trying to decide whether to lease or buy an item for your project. The daily lease cost is $120. To purchase the item, the investment cost is $1,000 and the daily maintenance cost is $20. How long will it take for the lease cost to be the same as the purchase cost?

Answer 1

Often, the lease vs. buy decision involves much more than just dollars (for example, training, conversion costs and resale value), but, since this problem asks that question, let's answer it:

 

"How long will it take for the lease cost to be the same as the purchase cost?"

 

Let x = number of days

     lease cost                         =                     purchase cost

           $120x                        =     purchase price  +   maintenance cost

 

   [note:  we assume that maintenance is included in the lease cost]  

             $120x                      =     $1000 + $20x

 

The math:

      $120x = $1000 + $20x

      $100x = $1000                       [subtract $20x from both sides]

          x = 10 

 

After 10 days, the dollars for a lease will equal the dollars for a purchase (and maintenance).

 

Check:

  Is       $120(10) = $1000 + $20(10)    ?

         $1200      =   $1000 + $200    ?

         $1200 = $1200    ?yes