Worked example
Suppose your collection station shows you gaining 500 Cash per minute (an illustrative number — read your own screen, since no public source documents real rates). A one-hour idle stretch projects to 500 × 60 = 30,000 Cash. If the next placement-limit upgrade in your own shop shows a price tag of 25,000, the upgrade pays for itself in 50 idle minutes if the extra placement adds more than ~8.3% to your rate (25,000 ÷ 30,000). That comparison — upgrade price divided by projected income, against the share of rate the upgrade adds — is the entire calculator, and every number in it comes from your own UI.
Gem math
Codes are the one place this game prints exact numbers. Both active strings pay Gems (15 Gems for VERSION7, 10 Gems for QUESTUPDATE — 25 total, checked 2026-10-03), but the redeem box stays locked until your account has played for roughly 30 minutes. Quests pay more Gems via the NPC next to the Gem Shop. Gems only spend in the Trendy Shop, so the honest framing is: Cash compounds inside your tower, Gems unlock cosmetics the Cash economy never touches.