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 to 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 areas. Since most items lose their value after a certain period of time when bought in this case knowledge to calculate depreciation can be 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;
…and the depreciation is;
Looking at the previous example we saw that;
That must mean that the calculation for the value after 10 years (let’s say) would be;
We can conclude that the formula for depreciated value is;
Using the depreciation formula
In the formula example, we’re going to use the formula we’ve discovered above.
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 can see that after 15 months the TV is valued at £400.82. It has dropped value by £999.18.
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.