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Financial Planning

Annuity Present Value Calculator

Find the present value of a stream of level or growing payments, such as a pension, lease or lottery annuity.

Your inputs

Results

Present value

$7,721.73

Sum of payments (undiscounted)
$10,000.00

✓Exact calculation — rounded only for display

Inputs are never added to links for financial, salary or health calculators.

What this calculator does

This values a series of future payments in today’s money, optionally with payments that grow at a constant rate each period.

Formula and method

Level: PV = PMT × (1 − (1 + r)^−n) ÷ r Growing: PV = PMT ÷ (r − g) × (1 − ((1 + g)/(1 + r))^n); if r = g, PV = n × PMT ÷ (1 + r) Multiply by (1 + r) for payments at the start of each period.

Worked example

Calculated by this tool with its default inputs:

Inputs

  • Payment per period: 1000 (any currency)
  • Discount rate per period: 5 %
  • Number of payments: 10
  • Payment growth per period: 0 %
  • Payments at: End of each period

Results

  • Present value: 7,721.73
  • Sum of payments (undiscounted): 10,000

How to read the results

Compare the present value with a lump-sum alternative: the larger value is better at your discount rate.

Assumptions and limitations

  • The first payment in the growing formula equals the payment entered.

Financial results are estimates based on the inputs and assumptions shown. They are not financial advice; confirm figures with your lender, provider or a qualified adviser before making decisions.

Questions

Why compare lump sum vs annuity at present value?

Because payments spread over time are worth less than the same total paid today.

Methodology and verification

Result type
Exact mathematical calculation (rounded only for display)
Formula version
1.0
Automated verification
4 reference and validation test cases, checked against independently computed values. The site cannot be built if any of them fail.
Editorial review
Awaiting human editorial review. The explanation was drafted with AI assistance; the formula and examples are verified by the automated tests above.

Privacy

Everything you enter is calculated in this browser and is not sent to Numerith or anyone else. Because this calculator can involve personal financial or health details, your inputs are never added to share links or saved to history. Privacy policy