Present value and future value are the two directions of the time value of money. Future value asks what a sum today will grow into, while present value asks what a future sum is worth right now. Learning to move fluidly between them lets you compare any two amounts arriving at different times on equal footing.
Future value: growing money forward
Future value tells you what an amount invested today will be worth after it compounds at a given rate. You multiply the starting sum by one plus the rate, raised to the number of periods. A single deposit left to grow, or a stream of regular contributions, both have a future value. This is the calculation behind projecting a retirement balance or a savings goal.
Present value: bringing money back
Present value runs the same math in reverse, discounting a future amount into today's terms. You divide the future sum by one plus the rate, raised to the number of periods. It answers how much you would need to invest now to reach a target later, or what a future payment is worth today. Bonds, pensions, and loan payoffs are all valued this way.
The discount rate is the hinge
The rate you choose drives both calculations and can change the answer dramatically. A higher rate makes future value grow faster and makes present value shrink faster. The right rate reflects realistic investment returns, inflation, and risk, so being honest about it matters. Small changes in the rate compound into large differences over long horizons.
Choosing which to use
Use future value when you have money now and want to know its later worth, such as projecting savings. Use present value when you have a future amount and want its value today, such as comparing a pension to a lump sum. Whenever two options pay off at different times, convert both to the same point in time before comparing. That common footing is the whole point of the exercise.
You need 50,000 dollars for a goal in 15 years and expect a 7 percent return. The present value, or what you must invest today, is about 18,100 dollars. Left alone at 7 percent, that 18,100 dollars grows back to 50,000 dollars in 15 years, which is its future value.
Key takeaways
- Future value grows a present sum forward using compounding.
- Present value discounts a future sum back to today.
- The discount rate strongly affects both figures, especially over long periods.
- Always convert amounts to the same date before comparing options.
Common mistakes
- Using an unrealistically high rate that flatters projections.
- Comparing a lump sum and a future stream without discounting to the same date.
- Forgetting to match the rate and the number of periods to the same time unit.
FAQ
Which rate should I use for present value?
Use a rate that reflects what you could realistically earn on similar-risk money, since that is your true opportunity cost.
Should present and future value use the same rate?
Within a single comparison, yes; using different rates for the two directions would make the amounts incomparable.