smc-1139-40-Find n

A sports car worth $150 000 is bought in December 2005.

In December each year, beginning in 2006, the value of the sports car is depreciated by 10% using the declining balance method of depreciation.

In which year will the depreciated value first fall below $120 000? (2 marks)

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`text(The value falls below $120 000 in the third year)`

`text{which will be during 2008.}`

Show Worked Solution

`text(Using)\ \ S = V_0(1-r)^n`

`text(where)\ \ V_0 = 150\ 000, r = text(10%)`

`text(If)\ \ n = 2,`

`S`	`= 150\ 000(1-0.1)^2`
	`= 121\ 500`

`text(If)\ \ n= 3,`

`S`	`= 150\ 000(1-0.1)^3`
	`= 109\ 350`

`:.\ text(The value falls below $120 000 in the third year)`

`text{which will be during 2008.}`