The value of the vehicle after 12 years of purchase will be $13,500.
Here, we are given that a vehicle purchased for $25,000 depreciates at a constant rate of 5%.
Therefore, the value of the vehicle after 1 year will reduce by-
25,000 × 5/100
= 250 × 5
= 1250
Thus, the value after 1 year will become = 25,000 - 1250 = 23750
In the same manner, the value will keep on reducing every year. Thus, the value after 12 years will become-
25,000 [tex](1- 5/100)^{12}[/tex]
= 25,000 [tex](1 - 0.05)^{12}[/tex]
= 25,000 [tex](0.95)^{12}[/tex]
= 25,000 × 0.54
= 250 × 54
= 13,500
Thus, the value of the vehicle after 12 years of purchase will be $13,500.
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