Question

Gareth has just remodeled his kitchen and wants to buy one of two stand-alone freezers. Consider the following table, which displays the prices, electricity costs, and lifespans of the two freezers he is considering:

Brand
Brand R
Brand S
Price
$575
$98
Avg. Cost/Wk
$3.17
$4.54
Lifespan
10 years
2 years

No matter which brand he chooses, Gareth will pay for the freezer on his credit card, which has an APR of 9.31%, compounded monthly. It takes Gareth eighteen months to pay off a Brand S freezer and four years to pay off a Brand R freezer. Assuming that Gareth makes no other purchases or payments with his credit card, over the next ten years, which brand of freezer will have a lower lifetime cost, and how much lower will it be? (Round all dollar values to the nearest cent.)
a.
Brand R will be $548.18 cheaper than Brand S.
b.
Brand R will be $712.40 cheaper than Brand S.
c.
Brand S will be $85.00 cheaper than Brand R.
d.
Brand S will be $164.22 cheaper than Brand R.

Answer 1

Answer: a. Brand R will be $548.18 cheaper than Brand S.

Work (summary):
- monthly interest rate r = 0.0931/12 = 0.0077583333...
- electricity for 10 years = 52 weeks/yr × 10 = 520 weeks
- Brand R electric = 3.17×520 = $1,648.40
- Brand S electric = 4.54×520 = $2,360.80

Brand R (one purchase, financed 48 months)
- monthly payment AR = 575·r / [1 − (1+r)^(−48)] → AR ≈ $14.39
- total paid for freezer = AR·48 ≈ $690.91
- 10-year lifetime costR = 690.91 + 1,648.40 = $2,339.31

Brand S (5 purchases at years 0,2,4,6,8, each financed 18 months)
- monthly payment AS = 98·r / [1 − (1+r)^(−18)] → AS ≈ $5.85
- total paid per freezer ≈ AS·18 ≈ $105.35
- total paid for 5 freezers ≈ 5·105.35 = $526.75
- 10-year lifetime costS = 526.75 + 2,360.80 = $2,887.93

Difference = costS − costR ≈ 2,887.93 − 2,339.75 ≈ $548.18 (Brand R is $548.18 cheaper).

Therefore choice (a) is correct.