# Depreciation

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This section explores depreciation. By the end you should be able to calculate the depreciated value and the amount of depreciation. You should have prior knowledge of working with percentages, decreasing percentages and good calculator skills.

Depreciation is the opposite of compound interest

…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 |

£13784.20

It has depreciated by;
£25000 – £13784.20 = £11215.80

…therefore the depreciation is;
£11215.80

## Depreciation formula

Looking at the previous example we saw that;End of 1

^{st}year, = 25000 × 0.82End of 2

^{nd}year = (£25000 × 0.82) × 0.82= £25000 × 0.82²

End of 3

^{rd}year = (£25000 × 0.82²) × 0.82= £25000 × 0.82³

= £13874.20

## Using the depreciation formula

We shall use the formula discovered above to work out some examples.
Example
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.

Answer

V = P(1 – r%)

^{n}= 1400(1 – 0.08)

^{15}= 1400 × 0.92

^{15}= £400.82

Explanation
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;

P = £1400

r = 8%

n = 15

V = ?

V = 1400(1 – 8%)

We can see that after 15 months the TV is valued at £400.82. It has dropped value by £999.18.
^{15}You have to be careful when working with depreciation. In some cases, depreciation may be calculated monthly, fortnight, weekly and maybe daily. So you have to be careful when working with problems involving depreciation and adjust the rate and number of calculations carefully.

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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