Question

A car is purchased for $23,000. Each year it loses 20% of its value. After how many years will the car be worth $7700 or less?

Answer 1

5 years at 7536.64$

Explanation:

1. 23000/5=4600

23000-4600=18400

2. 18400/5=3680

18400-3680=14720

3. 14720/5=2944

14720-2944=11776

4. 11776/5=2355.2

11776-2355.2=9420.8

5. 9420.8/5=1884.16

9420.85-1884.16=7536.64

Answer 2

We will use the formula

`\begin{gathered} A=P(1-r)^t \\ where \\ A=7,700 \\ P=23,000 \\ r=20\%=(20)/(100)=0.2 \\ t=? \end{gathered}`

Applying we have

`\begin{gathered} 7,700=23,000(1-0.2)^t \\ 7,700=23,000(0.8)^t \\ (0.8)^t=(7,700)/(23,000) \\ (0.8)^t=0.33478261 \\ \end{gathered}`

Taking log of both sides we have

`\begin{gathered} log(0.8)^t=log(0.33478261) \\ tlog(0.8)=log(0.33478261) \\ t=(log(0.33478261))/(log(0.8)) \\ t=4.9039009 \end{gathered}`

Hence the time is approximately 5 years