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Here we will learn about depreciation, including what depreciation is and how to solve problems involving depreciation.
There are also depreciation worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if youβre still stuck.
Depreciation is a form of repeated percentage change. It is the decrease of the value of an asset over a period of time.
The rate of depreciation of an asset is usually given as a percentage and we can use this to find the percentage multiplier to reduce the cost of the asset each year over its lifespan.
Depreciation is calculated using the same method as calculating compound interest.
Where is the percentage reduction and is the number of years.
For example, a new car originally costs The carβs value has an annual depreciation of Find the value of the car after years.
The multiplier needed to reduce a value by will be as we will be finding of the previous yearβs value.
The value of the car after years can be found by calculating,
So, after years the car is worth
In order to calculate a depreciation:
Get your free depreciation worksheet of 20+ simple and compound interest questions and answers. Includes reasoning and applied questions.
DOWNLOAD FREEGet your free depreciation worksheet of 20+ simple and compound interest questions and answers. Includes reasoning and applied questions.
DOWNLOAD FREEDepreciation is part of our series of lessons to support revision on simple interest and compound interest. You may find it helpful to start with the main simple interest and compound interest lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:
A boat is bought for It depreciates at a rate of per year. Find its value after years.
2Convert this percentage into a decimal to find the multiplier.
3Multiply the initial value by the multiplier raised to the power of the number of years (or given time period).
After years the boat is worth
A car is bought for For the first years it depreciates at a rate of per year. After that the depreciation rate changes to Find its value after years.
Subtract the depreciation rate from .
For the first years
For the remaining years
Convert this percentage into a decimal to find the multiplier.
Multiply the initial value by the multiplier raised to the power of the number of years (or given time period).
We need to apply the initial depreciation rate for years and then the second depreciation rate for the remaining years.
After years the car is worth
Notice that we give any answers involving money to decimal places.
A motorbike is bought for It depreciates at a rate of per year. After years the motorbike is worth Find
Subtract the depreciation rate from .
Convert this percentage into a decimal to find the multiplier.
Multiply the initial value by the multiplier raised to the power of the number of years (or given time period).
As we do not know the number of years but we do know the final value, we can use a trial and error method to find the value of
Too large
Too large
Too small
Correct
So years.
A common error is to think the multiplier for a depreciation rate is
It is important to subtract the depreciation rate from before finding the multiplier.
The multiplier for a depreciation is
A common error is to think that the amount the asset depreciates will remain constant each year. This is not the case. The depreciation rate may remain the same but as the value of the asset decreases so will the amount that is being subtracted.
If an asset is initially and reduced by is subtracted to give
If is reduced by is subtracted to give
1. What multiplier should be used for a depreciation of
2. What multiplier should be used for a depreciation of
3. A car is bought for and depreciates at a rate of per year. Find its value after years.
Rounded to decimal places this is
4. A car is bought for and depreciates at a rate of per year. Find its value after years.
5. A boat is bought for and depreciates at a rate of per year for the first years and then for the following years. Find its value after years.
6. A car is bought for and depreciates at a rate of per year. After years it is worth Find
1. What is the correct calculation to find the value of a car bought for after depreciating for years at a rate of per year?
Circle your answer.
(1 mark)
(1)
2. A house is bought for For years its value depreciates at a rate of per year.
For the further years it depreciates at a rate of per year. What is the value of the house after years?
(3 marks)
For a correct multiplier of or seen.
(1)
seen or calculating the amount after years.
(1)
(1)
3. The value of a car depreciates at a rate of per year.
After how many years will the car be less than half its original value?
(3 marks)
Multiplier of seen.
(1)
Attempts to apply powers to of multiplying a value by powers of .
(1)
years found.
(1)
You have now learned how to:
Depreciation is important in business. A company must be aware of its market value (book value), know what assets are tied into the business, and know exactly what is happening with its cash flow.
A balance statement (balance sheet) is a financial document that shows the value of a company or organisation.
An income statement is a financial document that shows the income and expenditure of a company.
A cash flow statement provides information on all of the different ways cash is coming in and going out of the business including business activities and investments.
Assets are very important to a business. An asset is a useful or valuable item or person. Three different types of asset include:
Assets within a business can be tax-deductible meaning that the tax is returned to the business. For tax purposes, a company should declare any assets that are tax deductible.
The useful life of the asset is the estimated number of years an asset is likely to remain in service. An assetβs useful life can be extended with the correct maintenance.
For example, vehicles have an annual service to extend their working life. The cost of a vehicle includes every debit needed to buy and maintain the vehicle: the purchase price (the original cost), maintenance, fuel, insurance, and tax.
Most tangible assets (for example, a piece of equipment) depreciate in monetary value over their lifetime. When the asset does not make money, the asset is a write off. A fixed asset depreciation schedule predicts the useful life of an asset. The residual value (salvage value) of the asset is an estimated value of an asset when it is no longer profitable to the business.
The total depreciation rate is an annual percentage of the total amount of depreciation for that year. The total amount of depreciation of a companyβs assets is known as accumulated depreciation. Loan amortisation allows for a business to borrow money when they face a large cost. Repayments are spread over months to years. This allows small businesses to buy assets that can help to make the business more profitable in the future.
Depreciation calculators help determine the life of an asset. These include:
Each of these methods have their own advantages and disadvantages in helping businesses determine their future success. For example, accelerated depreciation methods including the sum of the years digits recognise higher depreciation expenses during the earlier years of a business starting up.
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