Present Value vs Future Value
They are the same idea pointed in opposite directions. Future value projects what money you have today will be worth later, once it compounds: $10,000 at 6% for 10 years becomes about $17,908. Present value works backward — it takes a future amount and discounts it to what it is worth today: that same $17,908 due in 10 years is worth exactly $10,000 now. Future value multiplies money forward in time; present value divides it back.
The short answer
Both connect money at two points in time — they just travel opposite ways:
- Future value (FV) takes an amount you have today and projects it forward, adding compound growth: what will this be worth later?
- Present value (PV) takes an amount in the future and brings it backward, removing that growth: what is this worth today?
Because they are the same relationship run in reverse, any example works both ways: compound a present value forward and you get the future value; discount that future value back and you land on the original present value.
Try both directions: the time value of money calculator solves for present value or future value from the same inputs.
The two at a glance
| Future value | Present value | |
|---|---|---|
| Question it answers | What will today's money be worth later? | What is future money worth today? |
| Direction in time | Forward | Backward |
| Operation | Compounding (multiply) | Discounting (divide) |
| Formula | PV × (1 + r)n | FV ÷ (1 + r)n |
The third row is the heart of it: future value compounds money forward, present value discounts it back. Same rate, opposite operation.
One example, both directions
Take $10,000, a 6% annual rate and 10 years, and run it each way:
| Direction | You know | You solve for | Result |
|---|---|---|---|
| Future value | $10,000 today | Value in 10 years | $17,908 |
| Present value | $17,908 in 10 years | Value today | $10,000 |
Forward: $10,000 × 1.0610 = $17,908. Backward: $17,908 ÷ 1.0610 = $10,000. The two calculations are mirror images — whatever compounding builds up, discounting takes back down. That is why knowing any three of present value, future value, rate and time lets you find the fourth.
Why future money is worth less
Money you hold today can be invested, so a dollar now can grow into more than a dollar later. Flip that around and a dollar promised in the future is worth less than a dollar today. Here is what $10,000 received at various points in the future is worth right now, discounted at 6%:
| $10,000 received in | Present value today (at 6%) |
|---|---|
| 5 years | $7,473 |
| 10 years | $5,584 |
| 20 years | $3,118 |
| 30 years | $1,741 |
The further away the money, the less it is worth today — $10,000 promised in 30 years is worth only about $1,741 now. A higher discount rate shrinks those figures further, because your money would have grown faster in the meantime. This is the same compounding curve from how compound interest works, read from the other end.
When you use each
- Future value when you have money now and want to know what it becomes — projecting a savings balance, an investment, or a lump sum left to grow.
- Present value when you have a future figure and want its worth today — comparing a lump-sum offer against installments, valuing a retirement goal, or judging what a payout years away is really worth.
- Both together whenever you compare money at different times: discount everything to today, or grow everything to the same future date, so you are comparing like with like.
The future value formula covers the forward direction in depth, and the time value of money in Excel guide shows both in a spreadsheet.
The formulas
Future value compounds a present amount forward:
Present value discounts a future amount back:
Here r is the rate per period and n the number of periods. When money compounds more than once a year, r becomes the rate per period and n the total number of periods — monthly compounding uses r/12 and 12n. The two formulas are one equation rearranged, which is why every present value has a matching future value and vice versa.
Assumptions
- A single lump sum. The examples move one amount through time with no extra deposits or withdrawals.
- A constant 6% rate, used as both the growth rate and the discount rate so the two directions reconcile exactly.
- Annual compounding for a clean illustration. More frequent compounding changes the figures slightly; the calculator handles any frequency.
- No fees, taxes or inflation adjustment. A real discount rate would often fold in inflation and risk.
Frequently asked questions
The bottom line
Future value and present value are one relationship in two directions. Future value compounds today's money forward — $10,000 at 6% becomes $17,908 in 10 years. Present value discounts tomorrow's money back — that $17,908 is worth $10,000 today, and $10,000 promised in 30 years only about $1,741. Pick the direction that matches your question, use the same rate, and the two always reconcile.
Solve either direction with the time value of money calculator, or read the future value formula for the forward version in full.
Disclaimer: This page is for general educational purposes only and is not financial advice. The figures are illustrative and assume a constant rate; real discount rates vary with inflation, risk and compounding frequency. Consider speaking with a qualified financial professional before making decisions about your own money.