Question

The 2006 value of a car was $18,000. In 2016, it was worth $4000. If the annual percent of decay has been constant, what is the annual percent of decay?

Answer 1

`13.96\%`

Explanation:

we know that

The formula to calculate the depreciated value is equal to

`V=P(1-r)^(x)`

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

`P=\$18,000\\r=?\\x=10\ years\\V=\$4,000`

substitute in the formula

`\$4,000=\$18,000(1-r)^(10)`

Simplify

`(2/9)=(1-r)^(10)`

`(2/9)^(1/10)=(1-r)`

`r=1-(2/9)^(1/10)`

`r=0.1396`

convert to percent

`r=0.1396*100=13.96\%`