Find today's value of a future sum of money.
PV = FV / (1 + r)ⁿ.
Present value flips the future value question around: instead of asking what today's money will grow into, it asks what a future sum is worth right now, given that money available today can be invested and grown, while money promised in the future cannot start earning anything until it actually arrives. The mechanism is discounting — the future amount is divided down by a growth factor based on the assumed discount rate and the number of periods until it's received, which is mathematically the same compounding formula as future value, just run in reverse.
The discount rate chosen has an outsized effect on the result, and picking it is more judgment than formula: a higher discount rate produces a lower present value (because it implies today's money could grow faster elsewhere, making the future sum comparatively less valuable now), while a lower discount rate produces a higher present value. This is exactly why present value is the core tool behind comparing financial choices that pay out at different times — a lump-sum settlement offer versus a structured payout, or valuing a future pension versus a present cash equivalent — the comparison is only meaningful once both amounts are expressed in "today's money" using a consistently chosen discount rate.
Because money available today can be invested and start growing immediately, while money promised in the future can't start earning anything until it actually arrives. Present value 'discounts' the future amount down to reflect this lost growth opportunity, using an assumed discount rate and the number of periods until payment.
A higher discount rate produces a lower present value, because it assumes today's money could grow faster elsewhere, making the future sum comparatively less attractive now. A lower discount rate produces a higher present value. Since the discount rate is an assumption rather than a fixed number, it's worth testing a couple of reasonable rates rather than trusting a single result.
Comparing payout options that arrive at different times — for example, a lump-sum settlement offer versus the same total paid out over several years, or valuing a future pension benefit against an equivalent lump sum today. Both amounts need to be converted to present value using the same discount rate before they can be fairly compared.
Yes — present value and future value use the same underlying compound growth relationship between a value, a rate, and a number of periods. Future value projects a present amount forward in time; present value discounts a future amount back to today. Both answer the same underlying question about the time value of money from opposite directions.