a company spends $18,000 to purchase a piece of equipment. it has a useful life of 6 years and a salvage…

Explanation:

Step1: Recall straight - line depreciation formula

The formula for straight - line depreciation is $D=\frac{Cost - Salvage\ value}{Useful\ life}$, where $Cost$ is the initial value of the asset. Here, the company spends $18000$ to purchase the equipment, so the initial value is $18000$. The salvage value is $1350$ and the useful life is $6$ years. The annual depreciation amount $d=\frac{18000 - 1350}{6}=\frac{16650}{6}=2775$.

The explicit formula for a linear depreciation sequence (where $a_n$ is the value of the asset at year $n$) is $a_n=a_1+(n - 1)(-d)$. Here $a_1 = 18000$ and $d = 2775$.

Step2: Analyze each option

• Divide the salvage value by the years of useful life: This is incorrect. The salvage value is subtracted from the initial value first in the straight - line depreciation formula.
• Subtract the initial value from the salvage value: This is incorrect. It should be the initial value minus the salvage value.
• The explicit formula for the depreciation is $a_n=18000+(n - 1)(1500)$: This is incorrect as the annual depreciation amount $d = 2775\neq1500$.
• The initial value is $18000$: This is correct as the company spends $18000$ to purchase the equipment.
• The common difference is $3000$: This is incorrect as the annual depreciation amount $d = 2775\neq3000$.

Answer:

The initial value is $18000$ is a correct statement. There is only one correct statement among the given options based on the above - mentioned analysis. If we assume there is an error in the problem setup and we are just looking for statements that are factually correct about the given values at the start, the only correct one is "The initial value is $18,000$".