- The present value of an annuity is what a stream of future payments is worth today, at a chosen discount rate.
- The factor table below gives the present value of $1 per period; multiply by your payment to value any stream.
- Higher discount rates produce lower present values — which is exactly how annuity buyout companies profit.
- An ordinary annuity pays at period end; an annuity due pays at the start and is worth one period's interest more.
- This same math, run in reverse, is how insurers price the annuities they sell you.
Every annuity question is secretly a present value question. What a lump sum should pay you, what a payment stream is worth, whether a buyout offer is fair, how much a retirement needs — one calculation sits under all of it. This page gives you the formula, the full factor table computed exactly, and the two or three judgments the table cannot make for you.
The idea in one paragraph
A dollar arriving next year is worth less than a dollar today, because today's dollar can earn interest in the meantime. At 5%, a dollar due in one year is worth about 95.2 cents now; due in twenty years, about 37.7 cents. The present value of an annuity simply adds up those shrunken values across an entire stream of equal payments, producing one number: what the whole stream is worth today.
The formula
For an ordinary annuity — payments at the end of each period — the present value is:
PV = PMT × [1 − (1 + r)⁻ⁿ] / r
where PMT is the payment per period, r the interest rate per period, and n the number of periods. The bracketed factor is the PVIFA — present value interest factor of an annuity — and it is what the table below precomputes for payments of $1.
The table: present value of $1 per period
| Periods (n) | 2% | 3% | 4% | 5% | 6% | 7% | 8% |
|---|---|---|---|---|---|---|---|
| 1 | 0.9804 | 0.9709 | 0.9615 | 0.9524 | 0.9434 | 0.9346 | 0.9259 |
| 2 | 1.9416 | 1.9135 | 1.8861 | 1.8594 | 1.8334 | 1.8080 | 1.7833 |
| 3 | 2.8839 | 2.8286 | 2.7751 | 2.7232 | 2.6730 | 2.6243 | 2.5771 |
| 4 | 3.8077 | 3.7171 | 3.6299 | 3.5460 | 3.4651 | 3.3872 | 3.3121 |
| 5 | 4.7135 | 4.5797 | 4.4518 | 4.3295 | 4.2124 | 4.1002 | 3.9927 |
| 6 | 5.6014 | 5.4172 | 5.2421 | 5.0757 | 4.9173 | 4.7665 | 4.6229 |
| 7 | 6.4720 | 6.2303 | 6.0021 | 5.7864 | 5.5824 | 5.3893 | 5.2064 |
| 8 | 7.3255 | 7.0197 | 6.7327 | 6.4632 | 6.2098 | 5.9713 | 5.7466 |
| 9 | 8.1622 | 7.7861 | 7.4353 | 7.1078 | 6.8017 | 6.5152 | 6.2469 |
| 10 | 8.9826 | 8.5302 | 8.1109 | 7.7217 | 7.3601 | 7.0236 | 6.7101 |
| 12 | 10.5753 | 9.9540 | 9.3851 | 8.8633 | 8.3838 | 7.9427 | 7.5361 |
| 15 | 12.8493 | 11.9379 | 11.1184 | 10.3797 | 9.7122 | 9.1079 | 8.5595 |
| 20 | 16.3514 | 14.8775 | 13.5903 | 12.4622 | 11.4699 | 10.5940 | 9.8181 |
| 25 | 19.5235 | 17.4131 | 15.6221 | 14.0939 | 12.7834 | 11.6536 | 10.6748 |
| 30 | 22.3965 | 19.6004 | 17.2920 | 15.3725 | 13.7648 | 12.4090 | 11.2578 |
Factors for $1 received at the end of each period, discounted at the annual rate shown. Multiply by your payment amount. Computed from the formula above — exact to four decimals, and timeless: this table cannot go stale because it assumes the rate rather than promising one. For monthly payments, use the monthly rate (annual ÷ 12) and monthly period count in the formula itself, or use our calculator, which runs the same math with monthly compounding.
Three worked examples
Valuing a pension offer. A pension pays $24,000 a year for 25 years, and you are offered a lump sum instead. At a 5% discount rate the factor at 25 periods is 14.0939, so the stream is worth 24,000 × 14.0939 ≈ $338,254. A lump-sum offer well below that number is asking you to accept a much higher discount rate — which is a decision, not arithmetic, but now it is a visible decision.
Sizing a retirement need. You want $40,000 a year for 30 years and believe 4% is a safe earning assumption. Factor at 30 periods, 4%: 17.2920. You need roughly 40,000 × 17.2920 ≈ $691,681 today. Change the rate to 6% and the factor drops to 13.7648 — about $550,593. The spread between those two numbers is why the discount-rate assumption deserves more argument than it usually gets.
Reading a buyout offer. Someone offers $61,000 for your remaining $1,000/month over ten years. At 5% (monthly), the stream's present value is about $94,281. The offer is real money; it is also pricing your payments at roughly a 15% discount rate. The selling guide works this comparison in full.
Ordinary annuity vs annuity due
Everything above assumes end-of-period payments. If payments arrive at each period's start — an annuity due, like rent — each payment is discounted one period less, so the whole stream is worth more by one period's interest. The adjustment is a single multiplication: PV(due) = PV(ordinary) × (1 + r). At 5%, that is 5% more. Most insurance payouts and loan structures are ordinary annuities; leases and some structured payments are dues. Check which one you are holding before valuing it.
What the table cannot decide
The arithmetic is exact; two inputs are judgment. The rate: use what the money could genuinely earn at comparable risk — a current MYGA yield is an honest anchor, a hoped-for market return is not. The certainty of the payments themselves: a factor table assumes every payment arrives. Payments backed by an A++ carrier and payments promised by your cousin's business deserve different discount rates, and that difference — credit — is the entire subject of our carrier reviews.
One honest disclosure: this is the same mathematics an insurer uses, in reverse, when it prices an annuity for you — plus mortality tables for lifetime payouts, which is exactly why lifetime quotes cannot come from any table and period-certain figures can. That boundary runs through this whole site, and this page is the reason it exists.
Frequently asked
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