Depreciation
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…while compound interest increases the initial value each year by a given percentage, depreciation decreases the initial value each year by a given percentage. Depreciation is useful in many mathematical applications. Everyday items/properties when bought lose their value after a certain period of time. Knowing to how calculate depreciation is very useful.
Consider this example; The price of a new car is £25000. The price depreciates by 18% each year (p.a). Suppose we wanted to find its value at the end of 3 years. Here let’s use a table to calculate starting from year 1.
| Year 1 | £25000 x 0.82 = 20500 |
|---|---|
| Year 2 | £20500 x 0.82 = 16810 |
| Year 3 | £16810 x 0.82 = 13784 |
From the table we can see that 3 years after buying the car at £25000 the car is valued at;
It has depreciated by;
…therefore the depreciation is;
Depreciation formula
Looking at the previous example we saw that;
We can conclude that the formula for depreciated value is;
Using the depreciation formula
We shall use the formula discovered above to work out some examples.
Using the depreciation formula find the value of a TV after 15 months if it’s price while new is £1400 and it depreciates by 8% per month.
Let’s summarise the known variables and the unknown first then work out. We know that;
We’re trying to find the value of V. Using the known values we can conclude that;
We can see that after 15 months the TV is valued at £400.82. It has dropped value by £999.18.
THIS SUCKS U NEED QUARTERLY COMPOUNDED DEPRECIATION
other than that its cool
Hi,
Sorry about that. I will look into your suggestion.
one does not simply change the website.
Okay, seen as you’ve supplied all the information on how a retard can calculate a given set of numbers, could you tell viewers how one obtains the “given percentage” of depreciation, you’ve not included how one is suppose to work out this percentage, but you’ve given the percentages then told people how to calculate it from there … sigh
I think I see what you mean. The percentage is always an assumed value. You always have a record about how the original value depreciate over time i.e the percentage.
I think it will be necessary to include this part so thanks for the suggestion. In the car example above to calculate the percentage of depreciation over time you must have some record of how the prices have changed in the past. It is very easy. For example
In year 1 the price changed from £25000 to £20500
In year 2 it then changed from £20500 to £16810
In year 3 it then changed from £16810 to £13684
Using this past record we can work out by what percentage the value of the car decreases each year. Simply divide the current year value by the previous year and then subtract it from 1 since it is depreciation and multiply that by 100 for example;
In year 2 the price dropped from £20500 to £16810 so;
16810/20500 = 0.82, so; 1-0.82 = 0.18 (Note: 80% = 0.82 and 0.18 = 18%). Now multiply 0.18 by 100 to get 18%. You can see that it is the same as in the car example.
You can also use the depreciation formula derived above by rearranging it to find r%. You will need to have a few other values as well such as the initial value of the car for example. the depreciated value for example the value of the car in year 5.
I will definitely include this so thanks for the suggestion.
Hey thanks man. And these guys above a just being dicks. I thought it was pretty good and helped a lot.
Thanks again
Is there a way to solve for n without using logs if given the initial value,depreciation value, and depreciation % ?
i dont get how it becomes 0.82