Which expression correctly defines Average Annual Investment (AAI)?

• A. AAI = [P(n+1) + S(n-1)] / 2n
• B. AAI = P(n-1) + S(n+1) / 2n
• C. AAI = (P + S) / n
• D. AAI = P(n) + S / 2n

Answer: (A)

The expression for Average Annual Investment reflects how much capital is tied up each year when an asset's value decreases linearly from the initial investment P to the salvage value S over n years. Because the first year involves almost the full P and the last year only the salvage value S, the end values are weighted differently across the n years. Working through the linear decrease and averaging over the n years yields a weighted sum whose total per-year average is [P(n+1) + S(n−1)] divided by 2n. This matches the idea that early years contribute more to the average than later ones and gives a consistent result in edge cases (for example, when n = 1, the AAI equals P; if P = S, the AAI equals that common value).

The other forms don’t account for the timing weights or misplace the division, so they don’t produce the correct per-year average tied up in capital over the project life.