# Time Value of Money A dollar today is worth more than a dollar tomorrow — because today's dollar can be invested to grow, because inflation erodes the future dollar, and because the future is uncertain. This single principle is the foundation of all valuation: it is why [[Interest]] exists, why [[Bond]] and pensions and mortgages are priced the way they are, and why delay has a cost and patience a reward. Master it and the whole finance-valuation cluster (Present Value, Future Value, Net Present Value) falls out as arithmetic. ## The Mechanism The engine is *discounting*: to compare money across time, you translate future amounts into today's terms by dividing by a growth/discount rate. A promised $1,000 in ten years is worth much less than $1,000 now, and exactly how much less depends entirely on the discount rate you choose. That choice is the model's hidden politics. A high discount rate makes the future nearly worthless (the far-off benefit shrinks to almost nothing in today's terms); a low rate takes the future seriously. So every long-horizon decision — climate policy, infrastructure, pension funding, resource extraction — turns on a discount rate that is presented as a technical parameter but is actually a *moral choice about how much future people count*. The same arithmetic that prices a bond decides whether a hundred-year climate cost is worth preventing. ## KB Applications ### The discount rate as a moral parameter The vault's climate and long-horizon-policy files repeatedly surface the discount-rate fight — the technical-looking number that decides whether catastrophic future harms "pencil out" as worth preventing today. A high private discount rate (the market's) can rationalize running down a stable climate, a depleted aquifer, or crumbling infrastructure, because the future costs, discounted hard enough, look small now. Recognizing the discount rate as a value judgment smuggled into a formula is one of the most reusable moves the time-value model supplies — it converts "the numbers say don't invest" back into "we chose a number that says don't invest." ### Short-termism as institutionalized high discounting Quarterly earnings, election cycles, and engagement metrics all impose implicit high discount rates on institutions, systematically undervaluing the long-horizon investments that require patience (Local Minimum traps). Time value explains why the "efficient" market and the short-cycle politician both under-provide the future — not from stupidity but from the arithmetic of discounting under short horizons. ## See Also - [[Interest]] — the rate that does the discounting - [[Bond]] — time value priced into a security