Present Value Calculator

A professional-grade present value calculator for investors, analysts, and students. Compute the present value of a single future amount or an annuity with flexible compounding and optional inflation adjustment—fast, accurate, and fully accessible.

Calculation type
The future amount you will receive at time t.

Results

Present Value (PV) $0.00
Discount factor —
Total periods —
Periodic rate —
Notes —

Authoritative Content & Methodology

Data Source and Methodology

Authoritative sources:

  • Bodie, Z., Kane, A., Marcus, A. J. (2021). Investments, 12th ed. McGraw‑Hill. Chapter on Time Value of Money. Publisher link
  • U.S. SEC – Investor.gov: Compound Interest and Annuities methodology. Investor.gov calculators

Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.

The Formula Explained

Lump sum (discrete compounding):

PV = \( \dfrac{\text{FV}}{\left(1+\dfrac{r}{m}\right)^{m t}} \)

Lump sum (continuous compounding):

PV = \( \text{FV}\, e^{-r t} \)

Level annuity (ordinary):

PV = \( P \times \dfrac{1-(1+\frac{r}{m})^{-m t}}{\frac{r}{m}} \)

Annuity due:

PV = \( P \times \dfrac{1-(1+\frac{r}{m})^{-m t}}{\frac{r}{m}} \times (1+\frac{r}{m}) \)

Inflation adjustment (Fisher):

\( r_{\text{real}} = \dfrac{1+r}{1+i} - 1 \)

Where FV = future value, P = payment each period, r = annual nominal rate, m = compounding periods per year, t = years, i = inflation rate.

Glossary of Variables

  • Present Value (PV): The amount today equivalent to a future cash flow or series.
  • Future Value (FV): The amount received at a future date.
  • P (Payment): Fixed cash flow per period in an annuity.
  • r (Annual discount rate): Required return/interest rate per year (decimal form).
  • m (Compounding frequency): Number of compounding periods per year (1, 2, 4, 12, 365 or continuous).
  • t (Time): Number of years until payment(s).
  • Discount factor: PV/FV for a lump sum, or the annuity present value factor for series.
  • r_real: Real discount rate after accounting for inflation i.

How It Works: A Step-by-Step Example

Scenario: You expect $10,000 in 5 years. Your annual required return is 5% with monthly compounding.

  1. Inputs: FV = 10,000; r = 5% = 0.05; m = 12; t = 5.
  2. Compute periodic rate: \( r_p = r/m = 0.05/12 \).
  3. Compute total periods: \( n = m \times t = 12 \times 5 = 60 \).
  4. Compute PV: \( \text{PV} = \dfrac{10000}{(1 + 0.05/12)^{60}} \approx 7835.26 \).

Interpretation: Investing about $7,835.26 today at 5% compounded monthly should grow to $10,000 in 5 years.

Frequently Asked Questions (FAQ)

What discount rate should I use?

Use a rate reflecting your opportunity cost or the risk profile of the cash flow (e.g., your portfolio’s expected return, a WACC for projects, or a risk-free rate plus premium).

Does continuous compounding change the formula?

Yes. Lump-sum PV becomes \( \text{PV} = \text{FV} \, e^{-rt} \), where e is Euler’s number.

How is an annuity due handled?

An annuity due pays at the start of each period; multiply the ordinary annuity PV by \( (1 + r/m) \).

What if the rate is zero?

With r = 0, PV equals the undiscounted sum. Annuity PV is simply payment × number of periods.

Can I enter fractional years?

Yes. The calculator supports decimals for years to represent partial periods accurately.

Are taxes and fees included?

No. Results are pre-tax and exclude fees. Adjust your discount rate to reflect costs if needed.

Tool developed by Ugo Candido. Content verified by Finance Editorial Board.
Last reviewed for accuracy on: .