Chapter 5.4, Problem 21E

SUM-OF-THE-YEARS’-DIGITS METHOD OF DEPRECIATION One of the methods that the Internal Revenue Service allows for computing depreciation of certain business property is the sum-of-the-years'-digits method. If a property valued at C dollars has an estimated useful life of N years and a salvage value of S dollars, then the amount of depreciation $D_n$ allowed during the nth year is given by

$D_n=\left(C-S\right)\frac{N-\left(n-1\right)}{S_N}$ $\left(0\le n\le N\right)$

where $S_N$ is the sum of the first N positive integers. Thus,

$S_N=1+2+\dots N=\frac{N\left(N+1\right)}{2}$

Verify that the sum of the arithmetic progression $S_N=1+2+\dots N$ is given by $\frac{N\left(N+1\right)}{2}$.

If office furniture worth $6000 is to be depreciated by this method over $N=10$ years and the salvage value of the furniture is $500, find the depreciation for the third year by computing $D_3$.