Almost nothing in a plant happens once. Energy is saved every year, chemical is bought every year, a reserve is funded every year. That comb of equal arrows is $A$, and two factors move it — one to the far end of the timeline, one back to today.

Forward. $F = A\,\dfrac{(1+i)^{n} - 1}{i}$ — F equals A, one plus i to the n minus one, over i. $A$ is the equal amount deposited at the end of every period, $i$ the rate per period as a decimal, $n$ the number of deposits, and $F$ what the pile is worth immediately after the last one. The first deposit earns for $n-1$ periods, the second for $n-2$, the last for none at all — the factor totals every one of those in a single stroke.

Back. $\mathit{NPV} = A\,\dfrac{1 - (1+i)^{-n}}{i} - C_0$, where the fraction is the series present-worth factor, written (P/A, i, n) in the tables, and $C_0$ is the capital cost at year zero. $C_0$ takes no discounting at all — it is already standing at time zero, which is where present worth is measured. A positive NPV means the project beats the hurdle rate; it does not mean the project is free, and it does not mean the plant can afford it this year.

Know which one a question wants, because the two live at opposite ends of the same line. A-to-F asks what the money piles up to; A-to-P asks what the flow is worth today. Sinking funds and replacement reserves are A-to-F. Project appraisal is A-to-P, every time.

The named mistake, and it is the one worth branding: multiplying A by n. Ten years of $20,000 is $200,000 in cash and it is neither $200,000 of future value nor $200,000 of present worth. It is the money that passed through your hands, and it is the only figure in the family that ignores the rate entirely. Two quick rails keep you honest: the forward factor is always bigger than $n$, and the present-worth factor is always smaller. Anything else means a reciprocal went in backwards.