APFIVE Geometric Series Depreciation Model
A machine with an initial value of $$V_0$$ loses one-third of its value at the beginning of each year. The table shows the depreciation during each of the first three years. Which of the following gives an expression for the total depreciation of the machine over $$n$$ years?
| Year | Value Lost Calculation |
|---|---|
| 1 | $$V_0*(1/3)$$ |
| 2 | $$V_0*(1/3)*(2/3)$$ |
| 3 | $$V_0*(1/3)*(2/3)^2$$ |
A
The depreciation is given by an arithmetic series, so no closed-form geometric sum exists.
B
$$\frac{V_0*\left(1-\left(\frac{2}{3}\right)^n\right)}{\frac{2}{3}}$$
C
$$V_0*\left(1-\left(\frac{1}{3}\right)^n\right)$$
D
$$V_0*\left(1-\left(\frac{2}{3}\right)^n\right)$$
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