Value a future sum, a stream of payments, or both together — with a discount factor table and the compounding kept separate from the payment frequency.
Either one is enough — a single future sum, a stream of payments, or both together.
The discount rate is what your money could earn instead. A higher rate makes future money worth less today.
Estimates only. The discount rate is a judgement about what your money could otherwise earn and about risk — change it and the answer changes a lot. Figures are before tax and inflation.
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Money you get later is worth less than money you get now, because money in hand can earn something in the meantime. Present value puts a number on that gap. This calculator values a single future sum, a stream of payments, or both at once — which is what you need to price a bond, a lease or a settlement offer — and prints the discount factor table so you can see exactly where the number comes from.
Divide by the growth factor instead of multiplying by it: PV = FV ÷ (1 + r ÷ n)^(n × t). At a 5% discount rate, $10,000 received in five years is worth $7,835.26 today, because $7,835.26 invested at 5% would grow into $10,000 over that time. For a stream of payments the same logic is applied to each one and the results added, which the annuity formula does in one step: PV = PMT × (1 − (1 + i)^−m) ÷ i, where i is the rate one payment period carries. Present value and future value are the same equation solved from opposite ends.
Present value formula
Someone offers a lump sum instead of your monthly payments. Value the payments here and compare — the offer is only fair if it beats their present value.
The advertised jackpot is the sum of decades of payments. Its present value is far lower, which is why the cash option looks smaller than the headline.
A bond is coupons plus the face value at maturity. Enter both: if the discount rate is above the coupon rate, the price comes out below par, exactly as it should.
Value the lease payments today and compare against the purchase price. Set payments to the start of the period, which is how most leases actually run.
The table gives the present value of $1 at each rate and term. Multiply by any amount to value it without redoing the arithmetic — the reason these tables have been printed in textbooks for a century.
A lottery, a pension, a buyout: the only honest way to compare "$500,000 now" against "$50,000 a year for 20 years" is to value both today at the same rate.
It is a judgement about what you could earn instead and how risky the payment is, not a fact. $100,000 in eight years is worth $67,684 at 5% but only $40,388 at 12%. Change it and see.
They are two different settings. Discounting monthly payments at an annually-compounded rate is not the same as monthly compounding, and conflating them shifts the answer.
Payments received at the start of each period are worth (1 + i) more than the same payments received at the end — the difference between a lease paid up front and one paid in arrears.
At a 5% discount rate, $7,835.26. The discount factor is 0.783526, so every dollar received in five years is worth about 78 cents today. At 3% it would be $8,626.09 and at 10% only $6,209.21 — which shows how much the rate you pick matters.
PV = FV ÷ (1 + r ÷ n)^(n × t) for a single future sum, and PV = PMT × (1 − (1 + i)^−m) ÷ i for a level stream of payments, where i is the rate one payment period carries and m is the number of payments. When you have both, add them — they are independent.
A grid of discount factors: rows are periods, columns are rates, and each cell is the present value of $1 received at the end of that period. To value any amount you multiply it by the factor instead of recomputing the power. The table above is generated for your own term and includes your rate as its own column.
It is a judgement, not a lookup. The usual reasoning is what the money could earn in a comparable-risk alternative: a safe government-backed payment might be discounted near the Treasury yield, a payment that depends on a company staying solvent at something much higher. If you are comparing two offers, the rate matters less than using the SAME rate for both.
Present value discounts what comes in. Net present value discounts everything — the inflows AND the up-front cost — and nets them, so a positive NPV means the project beats your discount rate. NPV also allows a different cash flow each period, where this page assumes a level payment. Use the NPV calculator for uneven flows and an initial investment.
Because the advertised jackpot is the sum of payments spread over decades, not money that exists today. $250,000 a year for 20 years totals $5,000,000 nominally, but at a 4% discount rate it is worth about $3.4 million today. The cash option is roughly that present value — before tax.
Match the real arrangement. Rent and most leases are paid at the start (an annuity due); loan and settlement payments usually arrive at the end (an ordinary annuity). Starting payments are worth (1 + i) more, which on a three-year monthly lease is a noticeable difference.
Only if you are working in nominal terms, which is what this calculator does. If your future amounts are already in today's money, use a real rate instead — roughly your nominal rate minus expected inflation. The rule is to keep both sides consistent: nominal amounts with a nominal rate, real with real.