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Finance Calc Kit
Investments

Present Value Annuity Calculator

Calculate the present value of ordinary annuities, annuities due, growing annuities, and perpetuities with various compounding options.

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Present value (PV)

$7,721.73

Ordinary Annuity

How we calculated this

Open to see each step from your inputs to the result.

  1. Given values

    PMT = $1,000.00 per payment R = 5% (nominal rate per period) Compounding: 1 time(s) per period Payments: 1 per period, at end (ordinary)

  2. Apply formula

    i=rm=0.05001=0.050000iq=(1+0.050000)1/1−1=5.0000%n=q×t=1×10=10i = \frac{r}{m} = \frac{0.0500}{1} = 0.050000 \\[4pt] i_q = (1 + 0.050000)^{1/1} - 1 = 5.0000\% \\[4pt] n = q \times t = 1 \times 10 = 10

    PV = $7,721.73 Annuity Type: Ordinary Annuity

Report tool

What is the present value of an annuity?

The present value of an annuity is the lump sum today that equals a series of equal future payments discounted at a given interest rate. Investors, retirees, and lenders use this calculation to compare fixed payment streams against a single upfront amount. All math runs in your browser.

For a single future cash flow rather than a series, use the present value calculator. When payments continue forever, the perpetuity calculator applies the simplified infinite-horizon formula. For printable discount factors, see the present value annuity factor table.

Ordinary annuity formula

An ordinary annuity pays at the end of each period. With payment PMT, periodic rate i, and n payments:

PV=PMT×1−(1+i)−ni\mathrm{PV} = \mathrm{PMT} \times \frac{1 - (1 + i)^{-n}}{i}

An annuity due pays at the beginning of each period. Multiply the ordinary annuity result by (1 + i):

PVdue=PVordinary×(1+i)\mathrm{PV}_{\text{due}} = \mathrm{PV}_{\text{ordinary}} \times (1 + i)

Growing annuity and perpetuity

When payments grow at rate g each period and g is less than the discount rate i:

PV=PMT×1−(1+g1+i)ni−g\mathrm{PV} = \mathrm{PMT} \times \frac{1 - \left(\frac{1+g}{1+i}\right)^n}{i - g}

For a perpetuity (infinite payments), enter P or perpetuity as the number of periods. The formula simplifies to:

PV=PMTi\mathrm{PV} = \frac{\mathrm{PMT}}{i}

With payment growth g, the growing perpetuity formula is PV = PMT / (i - g), provided g is strictly less than i.

Worked example: ordinary annuity

You receive $1,000 at the end of each year for 10 years. The annual discount rate is 5%.

  • Periodic rate i = 5% = 0.05
  • Number of payments n = 10
  • PV = $1,000 × (1 - 1.05-10) / 0.05 = $1,000 × 7.7217 = $7,721.73

If the same payments occur at the beginning of each year (annuity due), multiply by 1.05 to get $8,107.82.

Compounding frequency

When interest compounds more than once per period, the calculator converts the nominal annual rate into an effective periodic rate before discounting. Select annual, semi-annual, quarterly, monthly, weekly, daily, or continuous compounding to match your loan, bond, or investment convention.

Frequently asked questions

What is the difference between an ordinary annuity and an annuity due?
An ordinary annuity pays at the end of each period. An annuity due pays at the beginning. Annuity due present value equals ordinary annuity PV multiplied by (1 + i).
How do I calculate present value of a perpetuity?
Enter P or perpetuity as the number of periods. Present value equals payment divided by discount rate: PV = PMT / i. For growing perpetuities, use PV = PMT / (i - g).
What happens when the growth rate equals the discount rate?
When g equals i in a growing annuity, the standard formula divides by zero. The calculator uses the limiting case: PV equals the sum of payments discounted individually.
How does compounding frequency affect present value?
More frequent compounding raises the effective periodic rate, which lowers present value for the same nominal annual rate. Monthly compounding produces a lower PV than annual compounding at the same stated rate.
When would I use a growing annuity?
Growing annuities model payments that increase over time, such as cost-of-living adjusted pensions, dividend streams with expected growth, or lease payments with scheduled escalators.
Are results stored on a server?
No. All calculations run in your browser. URL parameters let you bookmark and share specific scenarios without sending data to a server.

Resources and references

The formulas and methods in this calculator were checked against these independent sources.