Depreciation

Depreciation is the reduction in the value of an asset over time, typically due to wear and tear, obsolescence, or usage. Common assets that depreciate in value are cars and other motor vehicles.

Depreciation Formula:

V = P(1 - r)^t

where:

$V$ = Value of the asset after t years
$P$ = Initial value (purchase price) of the asset
$r$ = Depreciation rate (as a decimal)
$t$ = Number of years This formula is similar to the compound interest formula but with subtraction instead of addition, because the asset loses value each year.

Example

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A car costs €30,000 when purchased. The car depreciates over time with an annual depreciation rate of 20%. Calculate the car's value at the end of 3 years.

P=30,000, i=0.2,t=3

F=30,000(1-0.2)^3=€15,360

Example

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A television is bought for $€1500$ . After $3$ years, the estimated value is $€768$ . Calculate the percentage rate of depreciation.

F=768,P=1500,t=3

768=1500(1-i)^3

\frac{768}{1500}=(1-i)^3

\sqrt[3]{\frac{768}{1500}}=1-i

\frac{4}{5}-1=-i

-\frac{1}{5}=-i

\frac{1}{5}=20\%=i

Depreciation can also be calculated using the straight line method.

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Depreciation (straight line method) : Page 30

A=\frac{P-S}{t}

where $A$ is the annual depreciation amount, $P$ is the initial value, $S$ is the scrap value and $t$ is the useful economic life.

Example

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A construction company purchases a van for $€25,000$ . The asset has a useful lifetime of $4$ years before it is scrapped. The scrap value is estimated to be $€4000$ . The van is estimated to depreciate at $36.75 \%$ per year. Calculate the annual depreciation amount and the total depreciation after the $4$ years.

P=25000, S=4000,t=4

A=\frac{25000-4000}{4}=€5250

The total depreciation amount :

€5250 \cdot 4=21000

In general the straight-line method is used for assets that lose value evenly over time such as buildings, furniture etc. The reducing balance method is used for assets that lose more value in early years such as vehicles.

Depreciation Simplified Revision Notes for Leaving Cert Mathematics

Depreciation

Depreciation Formula:

A car costs €30,000 when purchased. The car depreciates over time with an annual depreciation rate of 20%. Calculate the car's value at the end of 3 years.

A television is bought for $€1500$ . After $3$ years, the estimated value is $€768$ . Calculate the percentage rate of depreciation.

500K+ Students Use These Powerful Tools to Master Depreciation For their Leaving Cert Exams.

Other Revision Notes related to Depreciation you should explore

Depreciation Simplified Revision Notes for Leaving Cert Mathematics

Depreciation

Depreciation Formula:

A car costs €30,000 when purchased. The car depreciates over time with an annual depreciation rate of 20%. Calculate the car's value at the end of 3 years.

A television is bought for €1500€1500€1500. After 333 years, the estimated value is €768€768€768. Calculate the percentage rate of depreciation.

500K+ Students Use These Powerful Tools to Master Depreciation For their Leaving Cert Exams.

Other Revision Notes related to Depreciation you should explore

A television is bought for $€1500$ . After $3$ years, the estimated value is $€768$ . Calculate the percentage rate of depreciation.