Question

A new car is purchased for 23900 dollars. The value of the car depreciates at 9.75% per year. To the nearest year, how long will it be until the value of the car is 7700 dollars?

Answer 1

11 years

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=\$23,900\\r=9.75\%=0.0975\\x=?\\V=\$7,700`

substitute in the formula

`7,700=23,900(1-0.0975)^(x)`

`(77/239)=(0.9025)^(x)`

Apply log both sides

`log(77/239)=xlog(0.9025)`

`x=log(77/239)/log(0.9025)`

`x=11\ years`