Engineering economy has almost no formulas in it. It has one idea — a dollar has a date attached — and a small family of factors for moving dollars between dates. Before any of them work, five letters have to mean something exact.

$P$ is a present sum: money at time zero, the day the project starts. $F$ is a single future amount: one payment, once, at the end of period $n$ — a resale, a rebuild, a one-off replacement. $A$ is an equal amount in every period, the same figure year after year — an energy saving, a service contract, a chemical bill. Read $A$ aloud as annuity or simply the annual; it is the letter that carries the repetition. $i$ is the interest or discount rate per period, a bare fraction with no currency on it — 8% enters every formula in this chapter as 0.08, never as 8. And $n$ is the number of periods, a plain count.

Two conventions, and they are not optional. First, i and n must share a period: an annual rate takes a count of years, a monthly rate takes a count of months, and mixing them is the single most common error on any economy paper. Second, the end-of-period convention: an amount $A$ in year 3 is assumed to land on the LAST day of year 3. Every printed compound-interest table in the world assumes it, which is why a saving that starts today is worth a little more than the tables say.

The cash-flow diagram is the tool. Draw a horizontal line, mark 0 at the left and $n$ at the right, and put an arrow at every date money moves — up for money coming in, down for money going out. $P$ is an arrow at 0. $F$ is a single arrow at $n$. $A$ is a comb of equal arrows at 1, 2, 3 and on. Nine times out of ten, drawing the diagram tells you which factor to reach for before you have written a symbol.

One nugget to carry. The letters are recycled between trades without apology: $C$ is a capital cost in a payback calculation and an initial cost in a depreciation schedule; $F$ is a future sum here and a fixed cost in a break-even calculation later in this chapter. The symbol never tells you what it is — the sentence around it does.