Finance & Money · 年金现值系数（Annuity Factor） · Updated 2026-10-25
What Is Annuity Factor?
Definition
The present value annuity factor PVA=(1-(1+r)^-n)/r tells you what "1 per period for n periods at rate r" is worth today. It compresses a whole family of discounting computations into a single table-lookup constant: loan payment = principal ÷ PVA (monthly basis), and pension gap = target income × PVA − current savings. Mortgages, annuity products and equipment leasing are all priced on this factor.
Formula
PVA = (1 − (1+r)^−n) / r
Worked Example
At 0.3% monthly (3.6% annual) over 360 periods, PVA≈217.8: a 1,000,000 loan costs ≈1,000,000÷217.8 ≈ 4,546/month — the origin of the annuity payment. Conversely, to draw 50k/year for 20 years at 3%, you need 5×14.88 ≈ 744k today.
Common Misconception
Assuming the factor table fits every annuity — PVA assumes end-of-period payments (ordinary annuity); for payments at the start of each period (rent, premiums) multiply by (1+r). Mixing them up skews results by roughly one full period of interest.
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