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Depreciation/Appreciation
Posted Date: 04 May 2008 Resource Type: Articles/Knowledge Sharing Category: Education
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Posted By: mark richards Member Level: Silver
Rating:  Points: 6
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Today’s topic will feature a combination of a variety of topics which includes percentages, depreciation/ appreciation and Geometric Progression. I have not taught Geometric Progression (G.P) but in this very chain of topics I will teach it.
I am going to teach depreciation/ appreciation today, it is the main topic but it involves percentages and (G.P) is a method which depreciation/ appreciation can be done! Let’s look at 2 types of depreciation questions! First we will look at the gradual depreciation type.
E.g. A house of value $500,000 depreciates annually by 2%. What will be the new value of the house 5 years from now, starting January 1st, 2008? This is the very exact question from 3 posts ago!
Solution: Method 1
Year | value at start | depreciation | end year value
1 | $500,000 | $500,000 x 2% =$10,000 | $490,000
2 | $490,000 | $490,000 x 2% =$ 9,800 | $480,200
3 | $480,200 | $480,200 x 2% =$ 9,064 | $470,596
4 | $470,596 | $470,596 x 2% =$9,411.92| $461,184.08
Therefore the value in the 5th year is $461,184.08
Note: the end year value for the 4th year is the value at start on the 5th year and 5 years from now means after for years. The S.A.T questions are all designed this way, so the trick in the question is the grammar and not the method how to solve it.
Solution: Method 2 (easier method)
Since the depreciation is 2% annually, the value after each year is 98% of the start.
After 1 year the value is $500,000 x .98= $490,000
After 2 years the value is $500,000 x .98 x.98= $480,200
After 3 years the value is $500,000 x .98 x.98 x.98=$470,596
After 4 years the value is $500,000 x (.98)^ 4 =$461,184.08
If you know the original value V, the rate of depreciation d% per annum, and the number of years n, the depreciated value is given by
V x ( (100 – d)/100)^ n
This is known as the depreciation/ appreciation formula.
Note: To do appreciation questions just change the minus sign to a plus sign!
Now let’s look at the other type of depreciation known as fixed appreciation.
E.g. A company vehicle bought for $125,000 in 2004 depreciates by a fixed value by 15% of the vehicle. What would be the value of the vehicle given by the company (book value) after 3 years?
Solution: Method
Value of the vehicle is $125,000.
Depreciation for the first year is $125,000 x 15%=$18,750
Depreciation for 3 years is $18,750 x 3=$56,250
Book value after 3 years is $125,000 - $56,250 =$68,750
This is the simplest for of depreciation. The next post I will show you how to use the (G.P) formula to do these questions.
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Responses
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| Author: m.v. subba raju 12 May 2008 | Member Level: Gold Points : 2 | Hi,
Explaining one topic in detail will help so many. Not only the students, but it will help the people who are writing competitive examinations, because the students can learn from lecturers or friends but for the people appearing for the competitive exams or departmental exams, they may not get all the relevant information. So, explaining like this will be very beneficial to the needy people.
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