Question

A graphic designer needs a laptop for​ audio/video editing, and notices that they can elect to pay

$3,500

for a Dell XPS​ laptop, or lease from the manufacturer for monthly payments of

$94

each for four years. The designer can borrow at an interest rate of

99​%

APR compounded monthly. What is the cost of leasing the laptop over buying it​ outright?

A.Leasing costs

$333

more than buying.

B.Leasing costs

$277

more than buying.

C.Leasing costs

$222

more than buying.

D.Leasing costs

$555

more than buying.

Answer 1

Answer : Correct Option is B.) Leasing costs $277 more than buying.

Reason :

Cost of Leasing Laptop is the present value of Annuity i.e

Present value of Annuity = Periodic Payment * {[1 - (1 + r )^(-n)]} / r

where n is the number of payments received i.e 4 years * 12 = 48 (As interest compounded monthly)

r is the interest per period i.e 9% / 12 = 0.75% or 0.0075

Present value of Annuity = 94 * {[1 - (1 + 0.0075)^(-48)]} / 0.0075

= 94 * {[1 - 0.698614]} / 0.0075

= 94 * {0.301386 / 0.0075}

= 94 * 40.18478

= 3777.369 or 3777

Cost of Buying = 3500 (Given)

Therefore Cost of Leasing is $277 (3777 - 3500) more than cost of buying.