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Sum-of-the-Years -Digits (SYD) The fourth method of computing depreciation is sum-of-the-years -digits. Like DDB, it is an accelerated method that allows more depreciation expense to be recorded in the early years of an asset s life and less in the later years. Like DDB, depreciation expense declines over the life of the asset, but unlike DDB, it declines by the same amount each year. To determine depreciation expense under SYD, the asset s cost (mi nus scrap value) is multiplied by a fraction. The numerator of the fraction is the years remaining in the asset s life, but in reverse order. It changes each year. The denominator is the sum of all the digits making up the life of the asset. It remains constant. For example, if a machine costs $17,000, has a scrap value of $2,000, and an estimated life of 5 years. The depreciable amount is $17,000 $2,000 = $15,000. To nd the fraction of this amount to be written off each year, proceed as follows: the numerator of the fraction for the rst year would be 5 (years in reverse). The denominator of the fraction would be 15, the sum of the year s digits (5 + 4 + 3 + 2 + 1 = 15). To determine the depreciation for the rst year, multiply $15,000 by (5/15). The cur rent year depreciation is $5,000. Partial-Year Depreciation If an asset is purchased during the year rather than at the beginning, each full year s depreciation must be allocated between the two scal years af fected to assure accurate reporting and accounting. The two scal years affected are the rst year and the nal year of depreciation.



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If BC and AD are the parallel sides of inscribed trapezoid ABCD in Fig. 6-51, find (a) mAB if mCD (b) mCD if mAB (c) mAB if mBC (d) mCD if mAD 85 y 60 and mAD mBC 170 80 (e) mjA if mjD (f) mjA if mjC (g) mjB if mjC (h) mjB if mAD 72 130 145 90 and mAB 84

One of the main drawbacks to using DTDs is that they do not allow for sophisticated datatyping. Take a second to refresh your memory: Attribute datatypes: ID, IDREF(S), CDATA, ENTITIES, NMTOKEN(S), and enumerated values Element datatypes: PCDATA and/or child elements

(6.11)





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A diameter is parallel to a chord. Find the number of degrees in an arc between the diameter and chord if the chord intercepts (a) a minor arc of 80 ; (b) a major arc of 300 . (6.11) Find x and y in each part of Fig. 6-52. (6.11)

Fig. 6-52

Find the number of degrees in the angle formed by a tangent and a chord drawn to the point of tangency if the intercepted arc has measure (a) 38 ; (b) 90 ; (c) 138 ; (d) 180 ; (e) 250 ; (f) 334 ; (g) x ; (h) (360 x) ; (i) (2x 2y) . (6.12)

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Find the number of degrees in the arc intercepted by an angle formed by a tangent and a chord drawn to the point of tangency if the angle measures (a) 55 ; (b) 671 ; (c) 90 ; (d) 135 ; (e) (90 x) ; (f) (180 x) ; (g) (x y) ; 2 (h) 31x . (6.12) 2 Find the number of degrees in the acute angle formed by a tangent through one vertex and an adjacent side of an inscribed (a) square; (b) equilateral triangle; (c) regular hexagon; (d) regular decagon. (6.12)

Once you know the four methods of depreciation, the next question is how to select the one that s most appropriate. Under generally accepted accounting principles (GAAP), businesses are encouraged to match the income an asset produces against its expense. This can be accomplished by selecting the correct depreciation method. Of the four depreciation methods discussed earlier, three are com pared in the table below. It is assumed that over a 5-year lifetime the as set was in operation for the following numbers of hours: 1,800, 1,200, 2,000, 1,400, 1,600. Cost of asset, $17,000; scrap value, $2,000.

Find x and y in each part of Fig. 6-53 (t and t9 are tangents). (6.12)

Fig. 6-53

If AC and BD are chords intersecting in a circle as shown in Fig. 6-54, find (a) mjx if mAB 90 and mCD 60 (e) mAB (f) mBC mCD if mjx mAD if mjx 70 65 160 2mBC

(6.13)

Fig. 6-54

Fig. 6-55

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