Question

Zeller industries bought a computer for $4600. It is expected to depreciate at a steady rate of 20% a year. When will the value have depreciated to $2000?

Answer 1

Answer: 3.733

Step-by-step explanation: if it asks for thousandths

Answer 2

About 3.73 yrs

Explanation:

This is a compound decay problem. Which has the formula:

`F=P(1-r)^t`

Where

F is the future amount (we want it to be 2000)

P is the present amount (which is 4600)

r is the rate of decay, depreciation (20% per year means 20/100 = 0.2)

t is the time in years (which we want to find)

Substituting, we find:

`F=P(1-r)^t\\2000=4600(1-0.2)^t\\2000=4600(0.8)^t\\0.4348=0.8^t`

Now we take natural log (Ln) of both sides and solve:

`Ln(0.4348)=Ln(0.8^t)\\Ln(0.4348)=tLn(0.8)\\t=(Ln(0.4348))/(Ln(0.8))\\t=3.73`

So, it will take about 3.73 years for the value to depreciate to $2000