AtlasCalcsUtility Calculation Suite
2026-09-23 6 min read

Present Value of Annuity Calculator

Today's value of equal future payments with steps and charts.

Calculator

Payment Per Period
$
Interest Rate (per period)(%)
%
Number of Periods

Results

Normal

PV of Ordinary Annuity

$7,360.09

Total Paid In

$10,000.00

Time Discount

$2,639.91

Live results update as you type — currently showing pv of ordinary annuity of $7,360.09. Replace the defaults with your own numbers.

Visualizations

PV vs Payments

7,360$PV
10,000$Total paid

Formula

Today’s value of equal end-of-period payments.

PV = PMT × (1 − (1+r)^−n) / r

Variables

SymbolNameUnitDescription
PMTPayment$Per period
rRate%Per period

Explanation

What the payment stream is worth today.

Step-by-Step Calculation

Follow each step to understand how the result is calculated from your inputs.

Step 1

PV = PMT × (1 − (1+r)^−n) / r

Result: $7,360.09
Step 2

Total payments = $1,000.00 × 10

Result: $10,000.00
Final Answer
$7,360.09

Worked Examples

See how the calculator works with different scenarios.

Scenario

The present value of annuity calculator run on the values above.

Inputs

payment:1000
rate:6
periods:10

Calculation

1. PV = PMT × (1 − (1+r)^−n) / r → $7,360.09 2. Total payments = $1,000.00 × 10 → $10,000.00

Result

PV of Ordinary Annuity: $7,360.09

Interpretation

$7,360.09 today for $1,000.00 × 10 at 6.00%.

Understanding Your Result

Your Result: PV of Ordinary Annuity: $7,360.09

What This Means

What the payment stream is worth today.

Why It Matters

$7,360.09 today for $1,000.00 × 10 at 6.00%.

Professional Interpretation

$7,360.09 today for $1,000.00 × 10 at 6.00%.

How this is calculated

Today’s value of equal end-of-period payments.

What drives the result

Compounding grows lump sums and streams forward; discounting shrinks them back. The rate is the exchange rate between today and tomorrow.

Recommendations

  • •Ordinary = end-of-period payments.
  • •Higher rates punish long annuities most.

Educational Content

Introduction

Money has a time price: a dollar today compounds forward and discounts backward. Annuities package that into streams, NPV/IRR judge projects, and DCF prices whole firms.

Concept Explanation

Compounding grows lump sums and streams forward; discounting shrinks them back. The rate is the exchange rate between today and tomorrow.

Applications

▸Saving and loan decisions
▸Project screening with NPV/IRR
▸Firm valuation with DCF

Benefits

  • •Comparable across timing
  • •Rate-explicit decisions
  • •Value linked to cash, not accounting

Limitations

  • •Constant-rate simplifications
  • •Even-flow shortcuts where noted
  • •Forecasts dominate DCF truth

Best Practices

  • •Match rate frequency to cash frequency
  • •Show ranges for DCF/IRR
  • •Annualize before comparing

Common Misconceptions

Myth: Nominal equals effective
Truth: Compounding gaps them — use EAR.
Myth: IRR alone decides
Truth: Scale and timing need NPV beside it.

Practical Tips

  • •Match rate frequency to payments.

Common Mistakes

Annual rate with monthly PMT
Convert first.

Assumptions

This calculator makes the following assumptions to provide estimates:

End-of-period: Ordinary timing.

Limitations

Be aware of these limitations when using this calculator:

Limitation: Constant-rate simplifications
Limitation: Even-flow shortcuts where noted
Limitation: Forecasts dominate DCF truth

Frequently Asked Questions

Answers to common questions about this calculator.

Higher rate?
Lower PV — future dollars discounted harder.
How accurate is the present value of annuity calculator?
It follows the stated TVM formula from your inputs. Match rate frequency to cash frequency for exact results.
Ordinary vs due?
Ordinary pays at period-end; due pays at start and is worth (1+r) more.
Nominal vs effective?
Nominal ignores compounding; effective (EAR) includes it — compare EAR.

Related Guides

Deepen your understanding with these educational resources.

Glossary

Technical terms used in mortgage calculations explained in plain language.

Present value
What a future sum is worth today after discounting.
Annuity
Equal payments each period for a fixed term.

Authoritative References

Trusted sources and standards referenced by this calculator.

Applicable Standards

End-of-period (ordinary) timing unless labeled dueMoney rounded for display only; math at full precisionEven annual flows where labeled; uneven timing needs period detail

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Page Information

Last Updated:

2026-09-23

Version:

2.0.0

License:

Free to use for educational and professional purposes.