APFIVE Geometric Series Depreciation Model
Which of the following expressions correctly represents the total depreciation (i.e., the sum of value lost) over $$n$$ years for a machine that loses one-third of its value each year, if the initial value is $$V_0$$?
| 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
$$V_0*\left(1-\left(\frac{2}{3}\right)^n\right)$$
C
$$V_0*\left(1-\left(\frac{1}{3}\right)^n\right)$$
D
$$\frac{V_0*\left(1-\left(\frac{2}{3}\right)^n\right)}{\frac{2}{3}}$$
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