Deferred Annuity Calculator
From a deferral period, annual payment, rate and years of payment, compute the present value of a deferred annuity.
輸入資料
計算結果
重點速覽：Deferred annuity PV = value an ordinary annuity (PMT x (1 - (1+r)^(-n))/r) at the end of a deferral period m, then discounted back m years: PV = [PMT x (1 - (1+r)^(-n))/r] / (1+r)^m. Example: defer 5y, then 10k/yr for 10y at 5% → PV at deferral end ≈77,217; PV today ≈60,466. Longer deferral or higher r → lower today's PV. WARNING: Ordinary annuity (end-of-year), fixed rate; real products add fees/mortality/guarantees. Education, not advice.
計算公式
普通年金現值 = 每期給付 ×[1 −(1 + r)^−n] ÷ r。
遞延年金現值 = 普通年金現值 ×(1 + r)^−d。
$$普通年金現值：$PV_{ord}=PMT\cdot\dfrac{1-(1+r)^{-n}}{r}$$$$$遞延年金現值：$PV = PV_{ord}\times(1+r)^{-d}$$$$$其中 $PMT$ 為每期給付、$r$ 為每期利率、$n$ 為給付期數、$d$ 為遞延期數。$$使用說明
- Enter the deferral years and payment years.
- Enter the annual payment and rate.
- View the PV at deferral end and the PV today.
每期給付、利率、給付期數與遞延期數對現值的影響
| 每期給付 (HK$) | 每期利率 | 給付期數 n | 遞延期數 d | 普通年金現值 | 遞延後現值 (HK$) |
|---|---|---|---|---|---|
| 1,000 | 5% | 10 | 0 | 7,721.73 | 7,721.73 |
| 1,000 | 5% | 10 | 5 | 7,721.73 | 6,050.18 |
| 50,000 | 4% | 20 | 10 | 679,516.32 | 459,056.88 |
理財情境案例
案例一：延後 5 年開始的年金現值
某年金每期 (年) 給付 HK$1,000，共給付 10 期，每期利率 5%,但要 5 期之後才開始給付 (遞延 5 期)。
第一步：普通年金現值 = 1,000 × [1 − (1.05)^−10] ÷ 0.05 ≈ HK$7,721.73（這是折算到給付開始前一期的價值）。第二步：遞延後現值 = 7,721.73 × (1.05)^−5 ≈ HK$6,050.18。
解讀：這組將在 5 年後才開始、連續 10 年每年給 HK$1,000 的年金，今天的公允價值約為 HK$6,050。若不遞延、立即開始給付，現值會是 HK$7,721.73；遞延 5 期讓現值少了約 HK$1,672,正反映『延後收款的時間成本』。
案例二：退休後才開始領取的年金
某人規劃退休金：預計退休後每年可領 HK$50,000、連領 20 年，但距離開始領取還有 10 年 (遞延 10 期),折現率假設 4%。
普通年金現值 = 50,000 × [1 − (1.04)^−20] ÷ 0.04 ≈ HK$679,516.32；遞延後現值 = 679,516.32 × (1.04)^−10 ≈ HK$459,056.88。
解讀：這份『10 年後開始、連領 20 年、每年 5 萬』的退休年金，換算成今天的價值約為 HK$459,057。這正是遞延年金在退休規劃中的典型用途——幫你把『未來一連串的領取』折算成『今天需要準備多少錢』,以評估目前的儲備是否足夠。遞延期越長 (越晚退休領取),折現後的現值就越低。⚠️ 實際年金產品的利率、費用、保證期與稅務各有不同，本計算器僅供教學與估算，不構成理財建議。
常見問題
What is a deferred annuity?
An annuity whose payments begin only after a deferral period. You commit/fund now, but the income stream starts later — typical in retirement planning (accumulate then draw) and some insurance/endowment products.
Why discount the deferral-end value back to today?
Because the annuity's value at the end of the deferral is a future figure; to compare it with money today you must discount it by the deferral period at the rate. That gives the true present cost/benefit of committing now for later income.
How do deferral and rate affect the PV?
Both push value further out and discount it more: longer deferral (larger m) and higher rate (larger r) each lower today's PV. Intuition — money received later is worth less now, and a higher discount rate makes future money worth even less.
What should Hong Kong users watch?
Local deferred annuities/endowments (e.g. Qualified Deferred Annuity policies under tax deferral) carry fees, surrender penalties and guarantee/annuity-rate features that this simplified model ignores. Compare with MPF, bonds and deposits; check the insurer's illustration and surrender value. The IFEC provides retirement-product education. Education, not advice.
How is this different from an immediate annuity?
An immediate annuity starts paying almost at once (no deferral, m ≈ 0), so its PV is just the ordinary-annuity value. A deferred annuity inserts a waiting period m before payments, adding the extra discount step. Deferred suits 'save now, retire later'; immediate suits 'need income now'. Both share the annuity valuation core; only the timing of the first payment differs.
相關工具
參考資料
內容審核：香港計算器財經團隊。計算邏輯與公式參考香港金融管理局（HKMA）及投資者及理財教育委員會（IFEC）之個人理財計算指引，結果僅供參考，實際以相關機構公佈為準。