Many financial decisions involve a stream of payments you will receive or owe: a pension, a structured settlement, an annuity contract, lease payments, a lottery prize paid over time, even the payments on a loan. To compare that stream with a lump sum, you need its present value — what the whole series is worth in today’s dollars. This calculator values level payments, growing payments and perpetuities, paid at either the start or the end of each period.
How to use the present value of annuity calculator
- Enter the payment amount and the payment frequency.
- Enter the number of payments, or tick perpetuity if the payments never stop.
- Enter the annual discount rate and its compounding.
- Choose whether payments are made at the end of each period (ordinary annuity) or the start (annuity due).
- Optionally add a payment growth rate per period for inflation-adjusted streams.
Annuity present value formulas
Multiply by (1 + r) for an annuity due. For a payment growing at g per period:
Letting n run to infinity gives the perpetuity formulas P ÷ r and P ÷ (r − g), which require r > g.
Worked example
A pension offers $2,000 a month for 20 years (240 payments) or a lump sum. You could earn 5.5% a year.
- Rate per month: 5.5% ÷ 12 = 0.458333%
- Annuity factor: (1 − 1.00458333−240) ÷ 0.00458333 = 145.372649
- Present value: $2,000 × 145.372649 = $290,745.30
Any lump-sum offer below about $290,700 is worth less than the payments at that rate. If the checks arrived at the start of each month, the value would be $292,077.88, and if they continued forever, $436,363.64.
Level vs. inflation-adjusted payments
Consider a pension of $24,000 a year for 25 years, discounted at 6%:
| Payment pattern | Present value |
|---|---|
| Level $24,000 a year | $306,800.55 |
| Starts at $24,000, rises 2.5% a year | $389,508.73 |
A cost-of-living adjustment adds more than a quarter to the value of the pension, which matters when comparing an inflation-protected pension with a fixed one.
Lottery-style prizes
Suppose a prize is advertised as $1,000,000, paid as 20 annual installments of $50,000, with the first payment immediately. At a 5% discount rate the installments are worth $654,266.04 today — about 65% of the headline figure. A cash option near that amount is roughly a fair trade at that rate; one well below it favors taking the installments.
Choosing the discount rate
The rate should reflect what the money could earn at similar risk. Payments guaranteed by a strong insurer or government deserve a rate near high-grade bond yields; payments from a weaker source deserve a higher one. Lower rates raise the present value, so try a few. The present value of annuity table shows factors for a range of rates at once.
The same math run in reverse gives the payment a lump sum can support — that is the annuity payment table and the basis of every loan payment. For a fixed annuity that accumulates first and pays later, see the deferred annuity calculator.
Valuations are estimates that depend on the discount rate you choose and ignore taxes, mortality and credit risk. They are not financial advice.
Frequently asked questions
What is the present value of an annuity?
It is the lump sum that, invested today at the discount rate, could fund the same series of payments exactly. It is also the most a rational buyer would pay today for the right to receive those payments.
How do I compare a pension lump sum with monthly payments?
Compute the present value of the monthly payments at a rate you could realistically earn, then compare it with the lump-sum offer. A lump sum below the present value means the payments are worth more, before considering life expectancy, inflation adjustments and the security of the payer.
What is a perpetuity?
An annuity whose payments never end. Its present value is simply the payment divided by the rate per period: $2,000 a month at a 5.5% annual rate (0.4583% a month) is worth about $436,364. Preferred stock and endowments are often valued this way.
Why is an annuity due worth more than an ordinary annuity?
Each payment arrives one period earlier, so each is discounted one period less. The present value of an annuity due equals the ordinary annuity's value times (1 + r).
How does the lottery cash option relate to this?
Lottery jackpots are advertised as the total of an annuity paid over many years. The cash option is close to the present value of those payments, which is why it is much smaller than the advertised jackpot.