Compound Growth Calculator
From initial principal, annual rate, years, frequency and contributions, compute the future value and total compounded growth.
輸入資料
計算結果
重點速覽：FV = PV x (1 + r/m)^(m·t) + PMT x ((1 + r/m)^(m·t) - 1) / (r/m); total principal = PV + PMT x m·t; growth = FV - principal. It handles both a lump sum and a recurring contribution (ordinary annuity, paid at period end). Example: 100k + 2k/mo at 6% monthly, 20y → FV ≈ 1.26m, growth ≈ 675k. WARNING: Fixed assumed return; real returns vary, not guaranteed; inflation and fees reduce real result. Education, not advice.
計算公式
未來值 FV = PV × (1 + r/m)^(m·t) + PMT × ((1 + r/m)^(m·t) − 1) ÷ (r/m)。
其中 PV 為初始本金、r 為年增長率、m 為每年複利次數、t 為年期、PMT 為每期供款。
投入本金總額 = PV + PMT × (m·t)；複合增長金額 = 未來值 − 投入本金總額。
$$未來值：$FV = PV\left(1+\dfrac{r}{m}\right)^{mt} + PMT\cdot\dfrac{\left(1+\frac{r}{m}\right)^{mt}-1}{r/m}$$$$$投入本金總額：$Principal = PV + PMT\times m\,t$$$$$複合增長金額：$Growth = FV - Principal$$$使用說明
- Enter the initial principal, annual rate and years.
- Pick the compounding frequency (e.g. monthly).
- Enter any periodic contribution to see FV, total principal and growth.
年增長率 6%、每月複利、20 年下不同投入方式的未來值
| 初始本金 (HK$) | 每月供款 (HK$) | 未來值 (HK$) | 投入本金 (HK$) | 複合增長 (HK$) |
|---|---|---|---|---|
| 100,000 | 0 | 331,020.45 | 100,000 | 231,020.45 |
| 0 | 2,000 | 924,081.79 | 480,000 | 444,081.79 |
| 100,000 | 2,000 | 1,255,102.24 | 580,000 | 675,102.24 |
理財情境案例
案例一：月供投資 20 年的複利成果
某人每月投入 HK$2,000 (初始本金為 0),假設年增長率 6%、每月複利，持續 20 年。
未來值 = 2,000 × [(1 + 0.06/12)^(12×20) − 1] ÷ (0.06/12) ≈ HK$924,081.79；投入本金總額 = 2,000 × 12 × 20 = HK$480,000；複合增長金額 = 924,082 − 480,000 ≈ HK$444,082。
解讀：20 年間實際只投入 48 萬本金，卻累積到約 92 萬，當中約 44 萬是複利滾出來的增長——增長金額幾乎等同投入本金。這說明『長期、有紀律的定期投入』搭配複利，能把小額月供滾成可觀的資產，時間越長效果越明顯。
案例二：本金與供款一起發力
承上例，若一開始已有 HK$100,000 本金，再加每月供 HK$2,000，同樣 6%、每月複利、20 年。
未來值 = 100,000 × (1 + 0.06/12)^240 + 924,082 ≈ 331,020 + 924,082 ≈ HK$1,255,102；投入本金總額 = 100,000 + 480,000 = HK$580,000；複合增長 = 1,255,102 − 580,000 ≈ HK$675,102。
解讀：起步本金 (10 萬) 與持續月供 (共 48 萬) 合共投入 58 萬，20 年後滾到約 126 萬，複合增長高達約 67.5 萬——增長金額已超過投入本金。這突顯『及早開始、本金愈多、投入時間愈長』的複利優勢。⚠️ 本計算器假設固定年增長率，實際投資回報會波動甚至虧損，結果僅供估算，不構成投資建議。
常見問題
What is the difference between compound and simple growth?
Compound growth reinvests each period's return so later returns earn on earlier returns ('interest on interest'); simple growth is on the original principal only. Over time, compounding accumulates far more.
Does a higher frequency always help?
At the same nominal rate, more frequent compounding gives a slightly higher FV, but with diminishing returns — annual to monthly is noticeable, monthly to daily is tiny.
When is the contribution paid?
This tool assumes an ordinary annuity — contribution at the end of each period. An annuity-due (paid at the start) would give a slightly higher FV.
What rate is realistic, and is the return stable?
There is no standard answer — it depends on asset class and risk. Conservative deposits/funds are low; equities/funds are higher but volatile. Use a long-term average and lean conservative; never treat the smooth fixed-rate result as a guarantee. Also factor inflation, fees (fund/management, trading) and tax. Run optimistic/neutral/conservative scenarios.
How do frequency and contribution timing affect the result?
Both matter, but less than amount, rate and time. Frequency: more frequent compounding lifts FV modestly (diminishing). Timing: start-of-period contributions earn one extra period versus end-of-period, so annuity-due FV is slightly higher. The dominant drivers of long-term results remain contribution, rate and time.
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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。