An annuity is a series of equal payments over time — a pension payout, an insurance product, or a structured settlement. Its present value is what that stream is worth today at a given discount rate.
Ordinary annuities pay at the end of each period; annuities due pay at the beginning (each payment therefore earns/discounts one extra period, worth exactly 1+i more). Compare a product's asking price against the present value before buying.
Frequently asked questions
What discount rate should I use?
A common choice is the risk-free long-term rate (what the payments could earn elsewhere with comparable safety). Higher rates shrink the present value — the same annuity is worth less when safe yields are high.
Annuity due vs ordinary annuity?
Annuity due pays at the start of each period, so every payment is discounted one period less (and compounds one more when valuing the future value) — it is always worth slightly more than the ordinary annuity.
中文说明
年金是按期等额的一系列给付——养老金领取、年金保险产品或分期给付协议都属此类。其现值回答的问题是：按给定折现率，这条现金流在今天值多少钱。
普通年金期末给付；先付年金期初给付（每期给付因此多计一期利息，价值恰为普通年金的 1+i 倍）。购买产品前，把报价与现值对比一下再决定。
常见问题
折现率应该取多少？
常见做法取长期无风险利率——即这笔钱在同等安全程度下另投他处能获得的收益。折现率越高现值越小：安全收益率高企时，同一份年金反而不值钱。
先付年金与普通年金有什么区别？
先付年金在每期期初给付，每笔给付少折现一期（算终值时多复利一期），因此价值恒略高于普通年金。