Present Value vs. Future Value: Pricing Money Across Time
October 21, 2026
Money today is worth more than the same amount later, because today's money can earn a return. Future value is what a sum grows to: FV = PV × (1 + r)^n. Present value is the reverse: PV = FV ÷ (1 + r)^n. At 5%, $10,000 received in 10 years is worth $10,000 ÷ 1.05^10 = $6,139 today, and $10,000 invested today grows to $16,289.
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Present value answers the question: how much would I need today to have a target sum later? To reach $10,000 in 10 years at 5%, you need $6,139 now. Future value answers what an amount today becomes: $6,139 grows to $10,000.
The higher the rate or the longer the time, the bigger the gap between the two numbers. At 8% the present value of $10,000 in 10 years falls to $4,632.
Annuities
A stream of equal payments has a present value of PMT × (1 − (1 + r)^−n) ÷ r. For $1,000 a year for 20 years at 6%, that is $1,000 × (1 − 1.06^−20) ÷ 0.06 = $11,470. The future value of the same stream is $1,000 × (1.06^20 − 1) ÷ 0.06 = $36,786.
This is the logic behind comparing a lump-sum payout with an annuity or pension: discount the payments at a reasonable rate and compare present values.
| Quantity | Formula | Result |
|---|---|---|
| PV of $10,000 in 10 yrs at 5% | FV ÷ 1.05^10 | $6,139 |
| FV of $10,000 in 10 yrs at 5% | PV × 1.05^10 | $16,289 |
| PV of $1,000/yr for 20 yrs at 6% | annuity formula | $11,470 |
| FV of $1,000/yr for 20 yrs at 6% | annuity formula | $36,786 |
Choosing the Rate
The discount rate should reflect what you could earn elsewhere with similar risk, or the cost of borrowing. A small change in rate has a large effect on long-term values, so test several rates. For safe cash flows, use a safe rate; for uncertain ones, a higher rate.
Frequently Asked Questions
What is the difference between present value and future value?
Present value is the worth today of a future sum, and future value is what today's sum will be worth later.
Why is a future dollar worth less than a dollar today?
Because a dollar today can be invested and earn a return, and because of inflation.
How do I choose a discount rate?
Use the return available on an alternative investment of similar risk.
Is a lump sum better than an annuity?
Compare present values at a sensible discount rate, and consider taxes, risk, and your need for stable income.