Present Value Calculator

PV = FV ÷ (1 + r ÷ m)^(m × t), and for continuous discounting PV = FV × e^(−r × t)

FV

The future value — the sum you expect to receive later

r

The discount rate a year, written as a decimal rather than a percentage

m

How many times a year the discounting is applied

t

How many whole years away the money is

PV

The present value — what that future sum is worth today

Use it for any decision where the money and the moment are separated: a lump sum offered now against a larger one later, a pension that starts at sixty-five, an invoice with a long payment term, a court settlement paid out over years. The rate is the hard part, and it is not the same number as the return on the thing being bought — it is your opportunity cost, what you could earn elsewhere at comparable risk over the same wait. Set it to zero and the page returns the future sum unchanged, which is the honest answer if you genuinely have no alternative use for the money. Read the discount share alongside the present value rather than on its own: 44.2% off sounds alarming until you notice that the wait was ten years and the alternative was earning 6% the whole time. Longer waits and higher rates both pull the present value down, and the pair compounds.

1. 100,000 arriving in ten years, discounted at 6%

   1. Discount factor: 1 ÷ 1.06^10 = 0.558395
   2. Present value: 100,000 × 0.558395 = 55,839.48
   3. Discount: 100,000 − 55,839.48 = 44,160.52
   4. Share of the future sum: 44,160.52 ÷ 100,000 = 44.2%

   This is the page's default. The discount share is the number worth sitting with: 44.2% of the money is the cost of the ten years, and it is not a fee anyone charges — it is what the wait is worth at a 6% opportunity cost.

2. 250,000 arriving in thirty years, discounted at 5%

   1. Discount factor: 1 ÷ 1.05^30 = 0.231377
   2. Present value: 250,000 × 0.231377 = 57,844.36
   3. Discount: 250,000 − 57,844.36 = 192,155.64
   4. Share of the future sum: 192,155.64 ÷ 250,000 = 76.9%

   A quarter of a million in thirty years is worth about what 55,839.48 is worth in ten — which is the whole point of the page. Money far enough away loses most of its present value even at a modest 5%, and here 76.9% of it has gone.

3. 50,000 arriving in five years, discounted at 8% compounded quarterly

   1. Periodic rate: 8 ÷ 100 ÷ 4 = 0.02 a quarter
   2. Periods: 4 × 5 = 20 quarters
   3. Discount factor: 1 ÷ 1.02^20 = 0.672971
   4. Present value: 50,000 × 0.672971 = 33,648.57
   5. Discount: 50,000 − 33,648.57 = 16,351.43, which is 32.7% of the future sum

   Discounting more often lowers the present value, exactly as compounding more often raises a future one. Here the quarterly discounting at 8% over five years takes off 32.7% of the money, against 25.3% for the same five years at 6% compounded annually in the table below.

The page discounts a single certain sum at a single certain rate, and almost nothing real is either. It cannot price a stream of payments — an annuity, a lease, a bond's coupons, a pension in drawdown — because each one needs its own discounting and its own date, and a page with one future value field has nowhere to put them. The rate is the weakest input: it is meant to be your opportunity cost, and nobody knows what a comparable-risk alternative will pay over thirty years, so any long-dated present value is a statement about the rate you chose as much as about the money. Nothing here adjusts for the chance that the money does not arrive at all, which is what a credit spread does in a market price; a promised 100,000 from a shaky counterparty is worth less than the same 100,000 from a government, and the page treats them identically. Tax is ignored on both sides — on the future receipt and on whatever you would have earned instead. Inflation is not modelled, and the discount rate is a nominal one, so if you want a present value in today's purchasing power you must use a real rate rather than a nominal one. Finally, the term is a whole number of years, and the amounts carry no currency symbol.

What is present value in plain terms?

It is what a sum of money arriving later is worth to you right now. If someone promises you 100,000 in ten years and you could otherwise earn 6% a year, that promise is worth 55,839.48 today — because 55,839.48 grown at 6% for ten years becomes 100,000. The other 44,160.52 is not a deduction anyone makes; it is what the ten years of waiting are worth at that rate.

How do I calculate present value by hand?

Divide the future sum by one plus the periodic rate raised to the number of periods. The periodic rate is the annual rate divided by how many times a year the discounting applies, and the number of periods is that same number times the years. For 100,000 in ten years at 6% with annual discounting that is 100,000 ÷ 1.06^10 = 55,839.48. Setting the discount rate to zero returns the future sum unchanged, which is the sanity check worth doing first.

What discount rate should I use?

The rate is your opportunity cost: what you could earn on money of comparable risk over the same wait. It is not the return on the thing you are buying, and it is not your borrowing rate unless you would actually borrow against the money. Government bond yields are the usual floor for a certain future sum; add something for the chance the money does not arrive. Because the rate is the input nobody can pin down, checking the answer at two rates and treating those as a range is more honest than picking one.

Why is a distant sum worth so little today?

Because discounting is compounding in reverse, and compounding is not a straight line. At 5%, 250,000 arriving in thirty years is worth 57,844.36 — 76.9% of it has gone. The effect is not linear in time: the same 250,000 arriving in ten years would be worth 153,478.31, so the last twenty years of the wait remove far more than the first ten. That is why long-dated promises and long-dated liabilities are so sensitive to the rate.

What is the difference between present value and discounted cash flow?

Present value is the calculation for one sum on one date; discounted cash flow is the same calculation applied to every payment of a stream and then added up. The present value formula is the building block — discount each future amount back to today at the same rate and sum the results, and you have a discounted cash flow. The difference is not in the mathematics but in how many dates are involved, which is why this page prices a single sum.

Does a higher discount rate always mean a lower present value?

Yes, for a positive future sum with a positive number of years, without exception. Raising the rate makes the divisor larger, so the present value falls and the discount share rises. The two inputs move the answer in the same direction, which is why a long-dated sum is doubly exposed: thirty years at 5% leaves 57,844.36 of 250,000, and the same thirty years at 8% leaves only 24,844.33.

• Compound Interest Calculator — the same equation run forwards instead of backwards — U.S. Securities and Exchange Commission (Investor.gov)
• H.15 Selected Interest Rates — the published yields a discount rate is chosen against — Board of Governors of the Federal Reserve System (United States)
• 12 CFR Part 1026, Appendix J — the periods-per-year convention behind the discounting frequency — Electronic Code of Federal Regulations (United States)