4. (20%)
The book value of year $n$ for the straight-line method can be rewritten as $B_n = \frac{(N-n)}{N}(I-S) + S$ with $\alpha = 1$, where $n = 1, 2, \dots, N$. If $\alpha = 2$ is used, the proposed method, no longer a straight-line method, has an acceleration effect.
(a) (10%) Derive the depreciation $D_n$ for a given year $n$ in terms of $I$, $S$, $N$, and $n$ for $\alpha = 2$.
(b) (10%) Compute the annual depreciation and the book values of each year for $I = \$10,000$, $S = \$2,000$, and $N = 5$ years for $\alpha = 2$
