University Car Wash built a deluxe car wash across the street from campus. The new machines cost $210,000 including installation. The company estimates that the equipment will have a residual value of $19,500. University Car Wash also estimates it will use the machine for six years or about 12,500 total hours. Actual use per year was as follows:

Year Hours Used
1 3,100
2 1,100
3 1,200
4 2,800
5 2,600
6 1,700

Prepare a depreciation schedule for six years using the double-declining-balance method.

Explanation:

Depreciation is the rate of the loss in value or decline of an asset over time until it reaches its salvage point where it is written off the books.

It is calculated either through the Straight Line Declining Balance method

(SLDB) or the Double declining balance method (DDB).

The DDB method (or accelerated depreciation) is twice the rate of depreciation of the SLDB.

Mathematically,

                                        DDB = 2 x SLBR x NBV

where SLBR is the rate of depreciation using the straight line method = (100% / lifetime of asset)

NBV is the Net Book Value of the asset

From the question, after year 1,

Car Wash value  = NBV - Depreciation

                           = $210,000 - (33.33% of $210,000)

                           =$210,000 - $70,000

                           = $140,000

Subsequent years would be

Year 2 = $140,000 - (33.33% x $140,000) = $93,333.33

Year 3 = $93,333 - (33.33% x $93,333)   = $62,228

Year 4 = $62,228 - (33.33% x $62,222) = $ 41,481.3334

Year 5 = $41,481.3384 - ( 33.33% x $41,481) = $27,659.286

Year 6 = $27,659.286 - (33.33% x $27,659.286) = $18,440.156

In summary,

Year   Initial book value  Depreciation Actual Depreciation         Net Book   Value

1         $210,000                  33.33%              $70,000                       $140,000

2        $174,000                   33.33%              $46,662                       $93,338

3        $93,338                     33.33%              $31,109                         $62,228

4        $62228                      33.33%              $20,740                       $41,487.

5        $41,487                       33,33%              $13,827                        $27,659

6        $27,659                      33.33%               $9,218                         $18,440

start by isolating the variable on one side by adding 43w^2 to both sides.   the equation will read:

25w^2+5=0

*subtract 5 from both sides*

25w^2=-5

*divide both sides by 25*

w^2=-1/5

*take the square root of both sides*

w=√(-1/5)

the square root of -1 is i.   the square root of 5 remains √5

the answer is i/√5.

hope this