Present Value Calculator — what future money is worth today

How it works

Two discounts, added. The single sum: PV = A ÷ (1 + r/k)^(k·y) — exactly the compound-growth formula inverted, so growing the answer back at the same rate reproduces the future amount to the cent. The stream: each payment discounts by its own distance, and the annuity closed form sums them — the same present-value arithmetic that prices a loan, which is why a published loan example doubles as this page's stream anchor. Enter either input alone or both together; the outputs keep the two parts visible. The horizon sweep runs 5 to 30 years and shows the two modes moving opposite ways: a lump further out is worth less, a longer stream is worth more, because it contains more payments.

Worked example

Both anchors are published pairs. The lump is the textbook case read backwards: $3,000 at 7% grows to $3,932.39 in four years (§8.02), so $3,932.39 due in four years is worth $3,000 today at that rate — the default inputs. The stream is published directly: LibreTexts works "$400 per month" at 12% for 4 years to a present value of $15,189.58 — the preset. Every other figure is the same two discounts at your inputs.

Frequently asked questions

What is present value?

The worth today of money that arrives later, at a chosen discount rate. A dollar promised in ten years is worth less than a dollar in hand — the rate quantifies how much less, compounding the gap year by year.

What discount rate should I use?

The rate that represents your alternative: a safe yield for certain money, a higher figure for risky promises, an expected return for investment comparisons. The result is only as meaningful as that choice, which is why the page treats the rate as an input rather than an assumption baked in.

Why does a payment stream get MORE valuable with more years?

Because more years means more payments — each new payment adds discounted value, even as the later ones are worth less each. A single fixed amount is the opposite: pushing it further out only deepens its discount. The sweep shows both behaviors on your inputs.

How is this related to loan amounts?

A loan IS a present value: the amount a lender hands over equals the discounted worth of your promised payments at the loan's rate. That is why the published loan pair — $400 a month for 4 years at 12% is $15,189.58 — verifies this page's stream formula verbatim.

Can I combine a lump sum and a stream?

Yes — enter both and the total is their sum, with each part shown separately. A bond is exactly that shape: coupon payments (the stream) plus the face value at maturity (the lump), discounted at the market yield.

How is this different from the future-value calculator?

Same arithmetic, opposite direction: future value pushes today's money forward at a rate, present value pulls future money back. Round-tripping through both at the same rate returns exactly where you started, which the tests here assert to the cent.

How accurate is this, and what does it exclude?

Exact for constant rates and end-of-period payments. It excludes risk (a discount rate can price it only crudely), taxes, and inflation as a separate force — a real-terms answer needs a real (inflation-adjusted) rate. For irregular cash flows at differing amounts, an NPV calculation generalizes this page.