How this instrument works
Present value answers a narrow question: if someone promises to hand you a fixed sum on a future date, what is that promise worth in your pocket right now? The formula is the compound-interest formula run backward. Instead of growing a sum forward by multiplying by (1 + r) once per period, present value shrinks a future sum by dividing by that same factor the same number of times. A dollar next year is worth less than a dollar today only because a dollar today can be put to work — lent, invested, or simply avoided as a debt — and grow into more than a dollar by the time next year arrives.
The rate r in the formula is doing the job of that opportunity cost, and it is chosen by the person doing the arithmetic, not derived from the sum itself. A pension actuary might use a rate tied to expected fund returns; a business appraiser might use a rate that reflects how risky the future cash flow is to collect. Change r and the same future sum is worth something different today — that sensitivity is the entire point of the exercise, not a flaw in it.
The number this instrument returns is a mathematical discount, not a market price. It says nothing about whether the future sum will actually be paid, what it will buy after inflation erodes it, or what fees and taxes might be taken out along the way. Those are separate questions the formula deliberately leaves for the person reading the number to answer.
- Enter the amount you expect to receive later in Future value, $.
- Set Discount rate per period, % to the rate you want to apply for each period that passes.
- Enter Number of periods — how many of those periods stand between now and the payment.
- Read Present value: the future sum divided by the compounding factor, in today's terms.
Worked example — a $1,100 payment one year out
Suppose a future value of FV = $1,100 is due in exactly one period, and the chosen discount rate is r = 10% for that period. The compounding factor is (1 + 0.10) raised to the power 1, which equals 1.10. Dividing 1,100 by 1.10 gives PV = $1,000 — meaning $1,000 placed at 10% for one period would grow into exactly $1,100, so the two sums are equivalent at that rate.
Stretch the same $1,100 out to two periods at the same 10% rate and the divisor becomes 1.10 squared, or 1.21, dropping present value to roughly $909.09. The extra period of waiting costs about $91 in today's terms, at that same rate. Raise the rate instead of the period count and present value falls faster still, which is why the discount rate, not the calendar, usually drives the biggest swings in this figure.
Questions
How does present value differ from future value?
They are the same relationship read in opposite directions. Future value starts with a sum today and multiplies it forward by the compounding factor; present value starts with a sum on a future date and divides it back by that identical factor. Feed the present value answer back in as a future value input with the same rate and period count and you recover the original figure exactly.
What discount rate should I enter?
That depends on what the future sum represents, and this instrument does not choose it for you. Analysts commonly tie the rate to the return the money could otherwise earn, or to the riskiness of actually collecting the future payment — a rate that is too low overstates today's worth, one that is too high understates it. Run the figure at a few different rates to see how sensitive the answer is.
Why does present value shrink as the number of periods grows?
Each additional period multiplies the divisor by another factor of (1 + r), so the discount compounds the same way growth does. Ten periods at a modest rate can cut a future sum's present value by half or more, because the division happens once per period, not once in total — the same mechanism that makes compound growth accelerate also makes compound discounting steepen.
Does this figure already account for inflation?
Only if the rate you entered already accounts for it. The formula treats r as a single discount rate and does not separate an inflation component from an opportunity-cost or risk component — if you want an inflation-adjusted answer, use a rate that has inflation built into it, or discount the sum twice with the two rates kept separate.
Why does my textbook or spreadsheet give a slightly different number?
The usual causes are a mismatched compounding frequency — annual versus monthly periods, for instance — or a rate entered as a whole number in one place and a decimal in another. Confirm that the period length in Number of periods matches the period the rate in Discount rate per period, % actually applies to, then recheck the figure.
Can present value be negative?
Not for a positive future sum at a rate above −100%, since dividing a positive number by a positive compounding factor always leaves a positive result. The formula rejects a rate at or below −100% outright, because that would mean dividing by zero or by a negative number, which has no meaningful present-value interpretation.
References
- SEC Investor.gov — Compound Interest Calculator
- IRS — Retirement plans, tax-advantaged savings basics
Read this first: This instrument shows arithmetic, not advice. Real offers add fees, taxes and terms that vary by lender and place — verify the figures against your actual paperwork before deciding anything.