Annuity Present Value
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%
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The present value of an annuity is the current worth of a series of future equal payments, discounted at a given rate. Used to value pension streams, lease obligations, lottery winnings, and structured settlements.
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Tip: To quickly check: multiply your monthly payment by the annuity factor for your rate and term. For a 6% annual rate over 20 years, the factor is about 139 — so $1,000/month has a PV of ~$139,000.
- 1PV = PMT × (1 − (1+r)^(−n)) / r
- 2PMT = periodic payment, r = discount rate per period, n = number of periods
- 3Higher discount rates reduce present value (future cash flows are worth less today)
- 4Annuity due (payments at beginning): PV × (1+r)
$1,000/month for 20 years at 5% discount rate=PV = $151,525Worth more as a lump sum today
$2,000/month pension for 25 years at 6%=PV = $255,282The actuarial value of the pension
| Rate/period | 10 periods | 20 periods | 30 periods |
|---|---|---|---|
| 1% (12% annual/monthly) | 9.47 | 18.05 | 25.81 |
| 0.5% (6% annual/monthly) | 9.73 | 18.99 | 27.79 |
| 0.33% (4% annual/monthly) | 9.82 | 19.60 | 28.93 |
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Fun Fact
When lottery winners choose a "lump sum" instead of the 30-year annuity, they typically receive about 60% of the advertised jackpot — the PV of 30 annual payments discounted at ~3–4%. The difference is the time value of money.
References
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