Answer:
[tex]5\ years[/tex]
Step-by-step explanation:
we know that
The formula to calculate the depreciated value is equal to
[tex]D=P(1-r)^{t}[/tex]
where
D is the depreciated value
P is the original value
r is the rate of depreciation in decimal
t is Number of Time Periods
in this problem we have
[tex]P=\$12,000\\r=9\%=0.09\\D=\$7,500[/tex]
substitute in the formula above and solve for t
[tex]\$7,500=\$12,000(1-0.09)^{t}[/tex]
[tex](7,500/12,000)=(0.91)^{t}[/tex]
Apply log both sides
[tex]log(7,500/12,000)=t*log(0.91)[/tex]
[tex]t=log(7,500/12,000)/log(0.91)=5\ years[/tex]
