Question

Timothy paid $27,000 for a new truck. If the value of the truck depreciates 11% for each year of his ownership, what is the minimum number of years needed for the vehicle's value to be less than $10,000.

Answer 1

The minimum number of years needed for the vehicle's value to be less than $10,000 is 9 years

SOLUTION:

Given, Timothy paid $27,000 for a new truck.

The value of the truck depreciates 11% for each year of his ownership,

We have to find what is the minimum number of years needed for the vehicle's value to be less than $10,000.

Let the number of years be n.

Now we can use the below formula to find the minimum number of years.

`\text { Present value }=\text { starting value } *\left(1-\frac{\text {rate of depreciation}}{100}\right)^{\text {number of years. }}`

Now, present value < 10000

`\begin{array}{l}{\text { Then, } 27000 *\left(1-(11)/(100)\right)^(n)<10000} \\\\ {\left(1-(11)/(100)\right)^(n)<(10000)/(27000)} \\\\ {(1-0.11)^(n)<(10)/(27)} \\\\ {0.89^(n)<0.37037}\end{array}`

Now, let us use trail and error method, put n = 8

Then, 0.3936 < 0.3703, wrong, so put n = 9, ⇒ 0.3503 < 0.3703 correct.

Hence, it takes 9 years.