My problem:
A computer bought for $3892$ is to be claimed as a tax deduction using straight-line depreciation of 15% of its original value each year until the total value has been claimed. Calculate the number of years that the equal deduction amounts will be claimed.
Textbook answer:
Okay first its said calculate the interest rate which is the 15% of $3892$. Okay this is easy but then this is where i am confused.
It said i need to contruct a formula (Arithmetic Progression) with inequality. (Which i disagree) It then said the deduction will take place until $tn < 0$; the value of the computer becomes less than $0$.
Let $t0 = 3892, t1 = 3892 -584$(interest)$= 3308$ and hence $a = 3308$ and $d = -584$
So the general formula= $tn =3308 - 584(n-1)$
The deduction will take place until$ tn < 0$
it said $3308 - 584(n-1) < 0$
My question us why? Why not just do $3308 - 584(n-1) = 0$ Where the number of years it takes to deduct the full value of the computer. What is the point of inequality in this case?
You need the inequality because the value may not be exactly $0$ at the end of any year. Suppose the value started at $\$5$ and the depreciation was $\$2$ per year. The formula would be $$ v = 5 - 2y $$ which is $0$ when $y=5/2$.