The Present Value of an Annuity Calculator discounts a stream of equal future payments back to a single value today, the calculation behind valuing a pension, a structured settlement, a lease's payment stream, or any series of level periodic payments. Enter the payment amount, the annual discount rate, the number of years and the payment frequency, and the calculator returns the present value of the entire stream.
Unlike discounting a single lump sum, an annuity present value has to account for every individual payment in the series, each discounted back from its own point in time, then summed together. The result answers a practical question: what would someone reasonably pay today in exchange for the right to receive this entire stream of future payments.
*These results are estimates for information only, not investment advice.*
Understand the present value annuity formula
The formula is Present Value = Payment x [(1 - (1 + i)^-n) / i], where i is the discount rate per period and n is the total number of payments.
This single equation sums the discounted value of every payment in the stream, with earlier payments discounted less (since they are received sooner) and later payments discounted more heavily.
Take a $100 payment received every year for 10 years, discounted at a 5% annual rate. Running those numbers through the formula gives a present value of approximately $772.17. This means an investor targeting a 5% annual return should be willing to pay about $772.17 today for the right to receive $100 a year for the next 10 years, and no more, to hit that target return exactly across the full stream of payments.
See how rate and term change the annuity's value
Raising the discount rate lowers the present value of the payment stream, since a higher required return means each future payment is worth less in today's terms.
Extending the number of payments raises the present value, since more total payments are being valued, though each additional payment further out contributes progressively less to the total because of the compounding discount effect.
The Present Value of an Annuity Calculator lets both rate and term be tested independently, which is useful for understanding, for example, how much less a 20-year payment stream is worth than double the value of an otherwise identical 10-year stream, since the second decade of payments is discounted more heavily than the first.
Value a pension, settlement or lease payment stream
This calculation directly answers questions like: what is a pension promising $100 a year for 10 years actually worth as a lump sum today, or what should a buyer reasonably pay to purchase the rights to a structured settlement's remaining payment stream.
In each case, the annual (or periodic) payment amount, an appropriate discount rate, and the remaining number of payments feed directly into this same formula.
Structured settlement buyers, pension plan actuaries and lease valuation professionals all rely on some version of this exact calculation, generally with more sophisticated adjustments for the specific product, to determine a fair present value for a stream of future payments.
Compare an annuity's present value against a lump sum offer
Someone offered a choice between a lump sum today and an equivalent stream of periodic payments can use this calculation to compare the two fairly.
If a $772.17 lump sum today is offered as an alternative to $100 a year for 10 years, and 5% is a realistic assumption for what that lump sum could otherwise earn, the two options are approximately equivalent.
If a lower lump sum is offered instead, the payment stream is the better deal at that discount rate; if a higher lump sum is offered, taking it and investing at the assumed rate would outperform the payment stream.
Know what this calculation assumes
This calculation assumes an ordinary annuity, with each payment occurring at the end of its period, a fixed discount rate held constant across the entire stream, and payments that occur exactly as scheduled with no missed or irregular payments.
Real pensions, settlements and leases may include cost-of-living adjustments, survivor provisions, or other features that this level-payment formula does not capture on its own.
Use the Present Value of an Annuity Calculator to value a straightforward stream of level payments, and adjust the underlying assumptions or seek a more detailed valuation for products with additional features like inflation adjustments or contingent payments.
Frequently asked questions
What is the formula for the present value of an annuity?
The formula is Present Value = Payment x [(1 - (1 + i)^-n) / i], where i is the discount rate per period and n is the total number of payments. It sums the discounted value of every payment in the stream.
What is the present value of $100 a year for 10 years at a 5% discount rate?
Discounted at a 5% annual rate, a $100 annual payment for 10 years has a present value of approximately $772.17, the amount someone should be willing to pay today for that entire payment stream to earn exactly a 5% return.
How is this used to value a pension or structured settlement?
This formula is used to value a pension or structured settlement by treating its periodic payment amount, an appropriate discount rate, and the remaining number of payments as the formula's inputs, producing a lump-sum equivalent value for the entire remaining stream.
Does a longer payment stream always have a higher present value?
Yes, extending the number of payments always raises the present value, holding the payment amount and rate constant, though each additional payment further in the future contributes progressively less due to the compounding discount effect.
What assumption does this calculation make about payment timing?
This calculation assumes an ordinary annuity, meaning each payment occurs at the end of its period rather than the beginning. An annuity due, with payments at the start of each period, would produce a slightly higher present value for the same inputs.
Summary
The Present Value of an Annuity Calculator discounts a stream of equal periodic payments to today's value using Present Value = Payment x [(1 - (1 + i)^-n) / i]. A $100 annual payment for 10 years, discounted at 5%, has a present value of approximately $772.17.
This is the calculation behind valuing pensions, structured settlements and lease payment streams as a single lump-sum equivalent. Figures shown are estimates, not investment advice.