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

Answer:

11 years

Step-by-step 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

$log(77/239)=xlog(0.9025)$  

$x=log(77/239)/log(0.9025)$  

$x=11\ years$