Present Value Calculator

Background.

A present value calculator answers the question every discounting problem in finance eventually reduces to: what is a future sum of money, or a stream of future payments, actually worth today? Present value (PV) is the mirror image of future value (FV) — instead of compounding a sum forward in time, it discounts a future sum backward, dividing it by (1 plus the periodic interest rate) raised to the number of periods between now and the payment date. The concept underlies bond pricing, lease valuation, lottery lump-sum-versus-annuity decisions, legal settlement structuring, pension buyout offers, and the whole discipline of discounted cash-flow analysis taught in every corporate-finance and CFA curriculum.

This calculator handles both halves of a present-value problem at once: a single future lump sum and a recurring future annuity payment, discounted together at one rate. Enter a future lump sum, a periodic payment, an annual discount rate, a time horizon, a compounding frequency, and whether payments arrive at the start or end of each period, and the tool returns the combined present value along with the two components broken out separately — so you can see exactly how much of the total came from the lump sum and how much came from the payment stream.

Quanta already publishes a future-value calculator that solves the same underlying time-value-of-money identity for four different unknowns — future value, present value, payment, or years — through a single "solve for" dropdown. This page exists alongside it deliberately, not as a duplicate. Someone who searches "present value calculator" is typically not thinking about future value at all; they have a known future number (a settlement offer, a bond's face value, a lease's payment schedule) and want to discount it back to today in the most direct interface possible, without first choosing a solver mode. The two pages compute the identical mathematics — FV = PV(1+i)^n + PMT×[(1+i)^n−1]/i rearranged for the variable you need — and this page's present value output will always match the future-value calculator's present-value solver mode for the same inputs. Use whichever framing matches how you are thinking about the problem; both link to each other for the alternate framing.

The distinction between ordinary annuities and annuity-due matters here just as it does for future value. An ordinary annuity assumes each payment lands at the end of its period — the standard convention for bond coupons, mortgage payments, and most textbook annuity formulas. An annuity-due assumes each payment lands at the beginning of its period — the convention for leases, rent, and insurance premiums. Because an annuity-due payment is, in effect, one period closer to today than the equivalent ordinary-annuity payment, its present value is always higher by a factor of exactly (1 plus the periodic rate). The calculator's Payment Timing toggle applies that factor automatically to the annuity portion only; it has no effect on the lump-sum portion, because a single lump sum has no "timing" ambiguity of its own.

Discount-rate selection deserves the same care here that it does in net present value analysis. For a corporate valuation, use the weighted average cost of capital. For a personal decision — a lottery payout, a structured settlement, a pension lump-sum offer — use your realistic opportunity cost, the return you could otherwise earn on money of comparable risk and liquidity. A higher discount rate always produces a lower present value, and the effect compounds with time: money forty years away discounted at 8 percent is worth barely a nickel on the dollar, while the same sum ten years away retains nearly half its face value. The calculator also reports the effective annual rate implied by your chosen nominal rate and compounding frequency, so two offers quoted on different compounding bases can be compared on equal footing.

Below the widget you will find the full derivation, a hand-verified worked example combining a lump sum and an annuity, FAQs on the FV/PV relationship, ordinary-versus-due timing, and choosing a discount rate, and citations to Brealey/Myers/Allen, Bodie/Kane/Marcus, the CFA Institute curriculum, and federal consumer-finance sources.

What is present value calculator?

Present value (PV) is the current worth of a future sum of money or stream of payments, given an assumed discount rate. It is the inverse operation of future value: where FV asks "what will this grow to," PV asks "what is that future amount worth right now." The two share the identical governing identity, FV = PV × (1+i)^n for a lump sum, rearranged to PV = FV / (1+i)^n. For an annuity — a series of equal payments — present value sums the discounted value of every individual payment; because each payment is progressively further in the future, each contributes progressively less to the total, forming a geometric series with the closed-form solution PV = PMT × [1 − (1+i)^−n] / i for an ordinary annuity, or that same figure multiplied by (1+i) for an annuity-due. Present value is the foundational concept behind bond pricing (a bond's price is the present value of its coupon payments plus its face value at maturity), lease accounting (the present value of future lease payments determines the liability recorded on a balance sheet), lottery payout decisions (comparing a lump-sum offer against the present value of an annuitized prize), and virtually every net-present-value capital-budgeting calculation, which is itself simply the present value of a project's future cash flows minus its upfront cost.

How to use this calculator.

1. 01Enter the Future Lump Sum you expect to receive or need at the end of the horizon. Set this to 0 if your scenario is a pure annuity with no single ending payment.
2. 02Enter the Future Periodic Payment — the recurring cash flow paid each compounding period. Set this to 0 for a pure lump-sum problem.
3. 03Set the Discount Rate as a nominal annual percentage. The calculator divides by the compounding frequency to get the per-period rate used in the discounting formula.
4. 04Enter Years — the time between today and when the lump sum and/or payments occur.
5. 05Choose the Compounding Frequency. This determines both how often the discount rate compounds and, for an annuity, how often payments are assumed to arrive.
6. 06Choose Payment Timing. End of Period (ordinary annuity) is the standard convention for bonds, loans, and most textbook formulas. Beginning of Period (annuity-due) is the convention for leases, rent, and insurance premiums, and produces a slightly higher present value for the annuity portion.
7. 07Read the four outputs: Present Value (the combined total), PV of the Lump Sum and PV of the Annuity (the two components broken out separately), Total Future Cash Flows (the undiscounted nominal total for comparison), and the Effective Annual Rate implied by your compounding choice.

The formula.

The calculator discounts two cash-flow types and adds the results together. Let i = r / m be the per-period discount rate, where r is the nominal annual rate (as a decimal) and m is the compounding frequency, and let n = years × m be the total number of periods. The present value of a future lump sum is PV_lumpsum = FV / (1 + i)^n — the lump sum divided by the same growth factor that would have compounded it forward. The present value of an ordinary annuity — equal payments made at the end of each period — is PV_annuity = PMT × [1 − (1 + i)^−n] / i, which is the standard formula for the present value of a finite, level payment stream. For an annuity-due (payments at the beginning of each period), every payment is effectively one period closer to today, so the ordinary-annuity formula is multiplied by (1 + i): PV_annuity_due = PMT × [1 − (1 + i)^−n] / i × (1 + i). The two present values are added together for the combined result: PV_total = FV / (1+i)^n + PMT × [1 − (1+i)^−n] / i × due_factor, where due_factor equals 1 for end-of-period payments and (1 + i) for beginning-of-period payments. When the per-period rate i equals zero, the annuity term is undefined by the formula above (division by zero), so the calculator instead uses the straight-line limit PMT × n × due_factor, which in the zero-rate case simplifies to exactly PMT × n since due_factor also collapses to 1 when i = 0. The effective annual rate, EAR = (1 + i)^m − 1, is reported separately so nominal rates quoted under different compounding conventions can be compared on equal footing. All arithmetic runs in arbitrary-precision Decimal.js math to avoid floating-point drift over long horizons and high-frequency compounding.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Brealey, R.A., Myers, S.C., and Allen, F. — Principles of Corporate Finance, 13th edition. Chapter 2 introduces present value and the opportunity cost of capital as the foundation of the whole textbook.
2. [2]Bodie, Z., Kane, A., and Marcus, A.J. — Investments, 12th edition. §5 covers the time value of money and present-value discounting as applied to portfolio and bond valuation.
3. [3]CFA Institute — CFA Program Curriculum, Quantitative Methods topic area: the time value of money, present value of a single sum, and present value of an annuity.
4. [4]U.S. Securities and Exchange Commission, Investor.gov — Compound Interest Calculator and accompanying investor-education materials on the time value of money.
5. [5]Mishkin, F.S. — The Economics of Money, Banking, and Financial Markets, 13th edition. Chapter 4 derives the present-value formulas for a lump sum and for an annuity.
6. [6]Consumer Financial Protection Bureau — Regulation Z (Truth in Lending) and Regulation DD (Truth in Savings), which require APR/APY disclosure so nominal rates on different compounding bases can be compared.