Depreciation

Some goods such as cars and computers decrease in value in time due to wear and deterioration. The depreciation formula allows us to determine the value of the vehicle in order to insure it. 

The depreciation formula is

A= P( 1 - R/100)^n

Where A = book value after n years

P = initial cost of the asset

R = rate of depreciation per annum

n = number of years for which the asset was depreciated. 

Amount by which asset depreciates:

D = P – A 

Eg. A Mazda car was bought in 2003 for $27,000. An insurance company decides to calculate its depreciation per annum as 5%. Determine:

(a) Its book value 3 years later 

Book value after 3 years 

𝐴=𝑃(1−𝑅/100)^𝑛

=$27,000(1−5/100)^3

=$23,149.13

Hence, the book value of the car after 3 years is $23,149.13.

(b) The amount by which it depreciates for the same period.

Amount D = P – A

=$27,000 - $23,149.13

=$3850.87

Hence, the car depreciates by $3850.87.

Solve and Show all working.

Calculate the book value of a new maxi taxi costing $44000 after 5 years if it depreciates each year by 13%.