In what year will the value of my car be $1000 if the starting price in 2007 was $30000? And as of right now the price is $16,500

Guest May 27, 2015

#3**+5 **

If the method of Depreciation used is declining balance Melody then this is the correct answer, nothing suspect about it.

Here's the relationship between straight-line and declining balance depreciation:

As you can see the straight line method will depreciate the asset a fixed amount every year until the asset is worth its final(residual) value whilst Declining balance will constantly adjust the amount of depreciation each year based on its book value for that year. This means that once the book value gets low then the depreciation charge is also low so it will take a longer time to reach a book value that is a small fraction compared to its original value when compared to straight-line depreciation.

Whether to use straight-line or the Declining balance method is up to the person/company to decide - each have their own pro's and con's

Brodudedoodebrodude
May 27, 2015

#1**+5 **

I'm assuming we're using Straight-line depreciation here, then:

$$DepreciationPerAnnum = \frac{Cost - ResidualValue}{UsefulLife}$$

2015-2007 = 8 years and current Total Depreciation = (30,000 - 16,500) = $13,500 then

DepreciationPerAnnum = $13,500 total / 8 years = $1687.5 depreciation per annum

Therefore:

$$1687.5 = \frac{30,000 - 1000}{UsefulLife} \\ UsefulLife = \frac{29,000}{1687.5} = 17.19 Years$$

Year When Value is $1000 = 2007 + 17Years = Year 2024.

Brodudedoodebrodude
May 27, 2015

#2**+5 **

$$\\16500=30000(1-r)^8\\\\

0.55=(1-r)^8\\\\

0.55^{1/8}=1-r\\\\

r=1-0.55^{1/8}$$

$${\mathtt{1}}{\mathtt{\,-\,}}{{\mathtt{0.55}}}^{\left({\frac{{\mathtt{1}}}{{\mathtt{8}}}}\right)} = {\mathtt{0.072\: \!005\: \!641\: \!200\: \!676\: \!8}}$$

$$r\approx 0.072\qquad $this is 7.2\%$$$

$$\\1000=16500(1-0.072)^n\\\\

0.060606060=0.928^n\\\\

log(0.060606060)=log(0.928^n)\\\\

log(0.060606060)=nlog(0.928)\\\\

n=\frac{log(0.060606060)}{log(0.928)}$$

$${\mathtt{n}} = {\frac{{log}_{10}\left({\mathtt{0.060\: \!606\: \!06}}\right)}{{log}_{10}\left({\mathtt{0.928}}\right)}} \Rightarrow {\mathtt{n}} = {\mathtt{37.516\: \!425\: \!994\: \!501\: \!126\: \!2}}$$

2015+37.5 = 2052

Mmm looks a bit suspect.

you better check it!

Melody
May 27, 2015

#3**+5 **

Best Answer

If the method of Depreciation used is declining balance Melody then this is the correct answer, nothing suspect about it.

Here's the relationship between straight-line and declining balance depreciation:

As you can see the straight line method will depreciate the asset a fixed amount every year until the asset is worth its final(residual) value whilst Declining balance will constantly adjust the amount of depreciation each year based on its book value for that year. This means that once the book value gets low then the depreciation charge is also low so it will take a longer time to reach a book value that is a small fraction compared to its original value when compared to straight-line depreciation.

Whether to use straight-line or the Declining balance method is up to the person/company to decide - each have their own pro's and con's

Brodudedoodebrodude
May 27, 2015