Present value of payments and supporting figures
r is the discount rate per payment period as a decimal and n is a whole number of payments. At a zero rate, present value equals payment times n. Beginning timing moves every payment one period earlier.
For a broader retirement balance and withdrawal scenario, use the Retirement Corpus Calculator with its separately stated income and inflation assumptions.
The formula
r is the discount rate per payment period as a decimal and n is a whole number of payments. At a zero rate, present value equals payment times n. Beginning timing moves every payment one period earlier.
Worked annuity present value example
Ten end-of-year payments of 1,000 discounted at 5% per year have a present value of 7,721.73. Beginning-of-year payments are worth 8,107.82 under the same assumptions.
How to use this calculator
- Enter payment each period, discount rate per period, number of payments.
- Set payment timing using the stated units or choices.
- Calculate and compare present value of payments, undiscounted payment total, difference from payment total.
Choosing inputs for annuity present value
Match the discount rate to the payment interval. Annual payments use an annual rate, while monthly payments need a rate appropriate for each month. This control deliberately accepts a per-period rate rather than guessing whether an annual quote is nominal or effective.
An ordinary annuity starts one period from now and pays at the end of every period. An annuity due starts now and pays at the beginning. Because each due payment arrives sooner, its present value is higher at a positive discount rate. Neither setting includes a separate final lump sum.
Interpreting present value of payments
The undiscounted total counts the cash payments without considering their timing. The difference from that total is the effect of the chosen discount rate, not a fee charged by a provider. Equal-payment valuation can help compare a payment stream with a lump sum, but it does not value insurance guarantees, mortality benefits, inflation protection, or the creditworthiness of an annuity issuer.
Assumptions & limitations
What this calculation assumes
- Payments are equal, equally spaced, and certain under the model.
- The discount rate remains constant and payments use one currency.
What to keep in mind
- Growing payments, fees, taxes, lifespan uncertainty, and contractual annuity benefits are excluded.
Common questions
Is this an insurance annuity quote?
No. It discounts the cash payments you enter and does not price an insurance contract.
What if the rate is zero?
The present value is simply the payment multiplied by the number of payments, for either timing choice.
Should I enter an annual rate for monthly payments?
Enter the discount rate per payment period. Convert an annual quote according to its nominal or effective convention before using monthly periods.
Sources & further reading
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