A graphic designer needs a laptop for audio/video editing,and notices that they can elect to pay $2900 for a Dell XPS laptop,or lease from the manufacturer for monthly payments of $79 each for four years.The designer can borrow at an interest rate of 7% APR compounded monthly.What is the cost of leasing the laptop over buying it outright?

Question

Quizplus · Accepted Answer

To find the cost of leasing, we need to find the total amount paid for the lease over 4 years.

Using the formula for the future value of an annuity (regular payments):

FV = PMT x (((1 + r)^n) - 1) / r

where:

PMT = monthly payment = $79 
r = monthly interest rate = 7% / 12 = 0.005833 
n = number of payments = 4 years x 12 months/year = 48

FV = $79 x (((1 + 0.005833)^48) - 1) / 0.005833 = $4,299.09

Therefore, the cost of leasing the laptop is $4,299.09.

Comparing this to buying the laptop outright for $2,900, we find that leasing costs:

$4,299.09 - $2,900 = $1,399.09

Therefore, leasing costs $399 more than buying outright.

So, the best choice is to buy the laptop outright if the designer has the available funds. However, if the designer cannot afford the lump sum of $2,900, leasing may be a viable option.

A Graphic Designer Needs a Laptop for Audio/video Editing,and Notices