A: The best way to see this is graphically on a cash flow diagram: you have $20K/year for 12 years, and then a cost increase kicks in for years 7–12. To build that profile, I decompose it as $20K for 12 years minus $5K for 6 years (years 1–6 only), not adding. Your version (15K + 5K) would give the right total for years 7–12, but you'd need to handle the two time periods correctly — the decomposition I use makes the P/A factor application straightforward.

A: In problem 21, costs jump to a new constant level — a one-time step increase that then holds steady. In problem 22, costs increase by a fixed amount each year, which is the definition of an arithmetic gradient. The phrasing '4K every year more than the previous year' signals a gradient; 'increases by 15K' with no year-over-year change signals a step to a new uniform series. Look for that distinction when you read the problem.