Transparent method
The formula
Worked example
Example inputs
How to interpret the result
The present value of an annuity is what a stream of future payments is worth today. Receiving $2,500 a month for 20 years adds up to $600,000, but discounted at 4 percent it is worth about $412,555, and the difference of about $187,445 is the value of waiting. The discount rate is the key input. A higher rate shrinks the present value fast, and a lower one raises it, so it should reflect the risk of the payments.
Before you rely on it
What to check
Pick a discount rate that matches the safety of the payer. A payment from a strong insurer is closer to a safe rate than one from a shaky company.
The common error
Where people go wrong with annuity present value calculator
Comparing the total of payments with a lump sum. The payments arrive over years, and a dollar later is worth less than a dollar now.
Sensitivity evidence
How annual discount rate changes the present value of payments
| Annual discount rate | Present value of payments | Undiscounted payments | Discounting difference |
|---|---|---|---|
| 2.0% | $494,185 | $600,000 | $105,815 |
| 3.0% | $450,777 | $600,000 | $149,223 |
| 4.0%worked example | $412,555 | $600,000 | $187,445 |
| 5.0% | $378,813 | $600,000 | $221,187 |
| 6.0% | $348,952 | $600,000 | $251,048 |
Every input, tested
Which input moves the present value of payments most
| Input | Tested from | To | Present value of payments at each end | Swing |
|---|---|---|---|---|
| Expected payment years | 15.0 years | 25.0 years | $337,980 to $473,631 | $135,651 (33%) |
| Monthly annuity payment | $2,250 | $2,750 | $371,299 to $453,810 | $82,511 (20%) |
| Annual discount rate | 3.0% | 5.0% | $450,777 to $378,813 | $71,964 (17%) |
Two variables at once
Present value of payments by annual discount rate and monthly annuity payment
| Annual discount rate \ Monthly annuity payment | $2,000 | $2,500 | $3,000 |
|---|---|---|---|
| 2.0% | $395,348 | $494,185 | $593,022 |
| 3.0% | $360,622 | $450,777 | $540,933 |
| 4.0% | $330,044 | $412,555 | $495,066 |
| 5.0% | $303,051 | $378,813 | $454,576 |
| 6.0% | $279,162 | $348,952 | $418,742 |
Step by step
The worked example, input by input
| Input | Value used |
|---|---|
| Monthly annuity payment | $2,500 |
| Annual discount rate | 4.0% |
| Expected payment years | 20.0 years |
| Present value of payments | $412,555 |
| Undiscounted payments | $600,000 |
| Discounting difference | $187,445 |
Where the inputs come from
Monthly annuity payment is the amount received each month, the discount rate reflects the return you could earn elsewhere, and expected payment years is the length of the stream. Use this to value a pension, a structured settlement, a lottery payout or an insurance annuity in today's dollars. The rate you choose is the biggest driver, so use a conservative rate that matches the risk of the payments.
When the result stops applying
The value depends on the discount rate, which makes a small change matter: a 6% rate lowers the example to about $349,000. The model assumes payments are certain and level, not adjusted for inflation or affected by the payer's credit risk. Taxes are ignored, and some streams have a different tax treatment from lump sums.
What to compare it with
Compare a pension offer with the pension lump sum versus annuity calculator, and see the annuity payout calculator for the reverse question. The present value calculator handles a single future sum, and the net present value page handles uneven cash flows.
People also ask
Frequently asked questions
Which discount rate suits an annuity stream?
A rate close to what you could safely earn, such as a high-grade bond yield. A higher rate assumes you could invest more aggressively, which lowers the present value.
Why is the present value less than the total payments?
Money received later is worth less than money today, because today's money can be invested, so future payments are discounted.
Can I use it to value a structured settlement?
Yes, as an estimate, but buyers of settlements use high discount rates, so offers are usually far below this figure.