The teacher chose option 2, the Starfish and it was valued at $35,200 after two months.
Step-by-step explanation:
Step 1; The Zoomba is priced at $60,000 and has an expected depreciation of 2% per month. So the annual depreciation is 12 months * 2% per month = 24% per year. The teacher plans to keep either car for two years do total depreciation is 2 years * 24% depreciation per year = 48 % in two years.
Value of car after two years = Buying price - Depreciation amount
= $60,000 - 48% of $60,000 = $60,000 - 0.48*$60,000 = $31,200
The car will be valued at $31,200 after two years. To determine how much value it has retained we divide the value in two years to the current value i.e $31,200 divided by $60,000 which equals 0.52 (52% of initial price)
Step 2; The Starfish is priced at $40,00 and will depreciate $200 every month. For a year it will depreciate 12 months * $200 per month = $2,400 a year. So for a total of two years a depreciaition of $4,800.
Value of car after two years = Buying price - Depreciation amount
= $40,000 - $4,800 = $35,200
The car will be valued at $35,200 after two years. To see the retained value we divide the depreciated value by the current value i.e. $35,200 divided by $40,000 which equals 0.88 (88% of the initial price)
Step 3; Of the two options, the Starfish retains more of its value over two years. So the teacher chose the Starfish over the Zoomba.
Answer:
D) The teacher chose the exponential option with an expected value of $36,946.82.
Step-by-step explanation:
Zoomba → exponential [tex]60,000(0.98)^{24}[/tex] = $36,946.82
Starfish → linear $40,000 − 200(24) = $35,200
