Answer:
11 years
Step-by-step explanation:
we know that
The formula to calculate the depreciated value is equal to
[tex]V=P(1-r)^{x}[/tex]
where
V is the depreciated value
P is the original value
r is the rate of depreciation in decimal
x is Number of Time Periods
in this problem we have
[tex]P=\$23,900\\r=9.75\%=0.0975\\x=?\\V=\$7,700[/tex]
substitute in the formula
[tex]7,700=23,900(1-0.0975)^{x}[/tex]
[tex](77/239)=(0.9025)^{x}[/tex]
Apply log both sides
[tex]log(77/239)=xlog(0.9025)[/tex]
[tex]x=log(77/239)/log(0.9025)[/tex]
[tex]x=11\ years[/tex]
