年數合計(sum-of-the-years'-digit) - 會計

Maserati Corporation purchased a new machine for its assembly process on
August 1, 2012. The cost of this machine was $150,000. The company estimated
that the machine would have a salvage value of $24,000 at the end of its
service life. Its life is estimated at 5 years and its working hours are
estimated at 21,000 hours. Year-end is December 31.

Instructions
Compute the depreciation expense under the following methods. Each of the
following should be con-sidered unrelated
(c)Sum-of-the-years’-digits for 2013.

買一個新機器在8/1/2012，成本150,000，殘值24,000，使用5年

問: 2013年數合計法算出來的折舊費用?

A算法
126*5/15*5/12 =17.5 Aug 1~Dec 31,2012
126*5/15*7/12+126*4/15*5/12 =24.5+14 =38.5 2013
126*4/15*7/12+126*3/15*5/12 =19.6+10.5 =30.1 2014
126*3/15*7/12+126*2/15*5/12 =14.7+7 =24.7 2015
126*2/15*7/12+126*1/15*5/12 =9.8+3.5 =11.3 2016
126*1/15*7/12 =4.9 Jan~July 31,2017
total=127 127
B
126 *5/15=42000 *5/12= 17.5 Aug 1~Dec 31,2012
126 4.58/15 = 38.472 2013
3.58/15 = 30.072 2014
2.58/15 = 21.672 2015
1.58/15 = 13.272 2016
0.58/15 = 4.872 Jan~July 31,2017
total= 125.86

B算法是教授給出來的，上課時來不及問，但剛坐車越想越怪...
想請問B的道理是...?? 雖然最後累計折舊會相近，但2015和2016差的有點大...
為什麼可以這樣4/3/2/1/0 + 0.58? 我知道0.58=7/12，但想不通為何這樣可以表示
各年度折舊費用?

還有個問題，就算按正常的算法A，150-127=23
跟預設殘值有誤差是跨年度折舊，計算過程的進位很容易造成的?

先感謝版友解答!

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