Question

The value of an industrial machine has a decay factor of 0.75 per year. After six years, the machine is worth 7500. What was the original value of the machine?

Answer 1

I found: `30,720,000` BUT I used a cumulative effect impacting `0.75` upon the reduced values of each year.

Explanation:

Call the original value `x`;
after the first year the value will become:
`x-0.75x`
after the second year:
`(x-0.75x)-0.75(x-0.75x)=(x-0.75x)(1-0.75)`
after the third year:
`[(x-0.75x)(1-0.75)]-0.75[(x-0.75x)(1-0.75)]=(x-0.75x)(1-0.75)(1-0.75)=(x-0.75x)(1-0.75)^2`
so basically we have that after the nth year:

`(x-0.75x)(1-0.75)^(n-1)`

in 6 years:
`(x-0.75x)(1-0.75)^5=7500`
`0.25x=7500/(1-0.75)^5`
so:
`x=30,720,000`