Question

The value of a specific piece of machinery depreciates at a rate of 10% per year.

The
initial value of the machinery is $400.
After how many years will this piece of machine be worth less than $200?

Answer 1

7th year

Explanation:

A small algorithm:

initial value : 400

1st year : 10% of 400 = 40 -> 400-40 =360

2nd year : 10% of 360 = 36 -> 360-36 = 324

3rd year : 10% of 324 = 32.4 -> 324-32.4 = 291.6

4th year : 10% of 291.6 = 29.16 -> 291.6-29.16 = 262.44

5th year : 10% of 262.44 = 26.244-> 262.44 -26.244 = 236.196

6th year : 10% of 236.196 = 23.6196 -> 236.196-23.6196 = 212.5764

7th year : 10% of 212.5764 = 21.25764 -> 212.5764-21.255764 = 191.31876 <200

the piece of machine is worth less than 200$ after 7 years