What is compound interest?

Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. It's the mechanism that makes money grow non-linearly over time — earnings earn earnings.

How is it different from simple interest?

Simple interest is calculated only on the original principal (Interest = P × r × t). Compound interest reinvests each period's interest, so the balance grows at an accelerating rate. Over long horizons the gap is dramatic.

What does compounding frequency change?

It's the number of times per year interest is added to the balance. More frequent compounding produces slightly higher growth at the same nominal rate — but the marginal benefit shrinks fast as frequency increases. Monthly is meaningfully better than annual; daily is barely better than monthly.

What is continuous compounding?

The mathematical limit of compounding infinitely often, given by A = P × e^(r·t) where e ≈ 2.71828. It sets an upper bound on what any other compounding schedule can produce at the same rate.

How do I use this calculator?

Enter the principal (starting amount), the annual interest rate as a percentage, the time in years, and pick a compounding frequency. The final amount and total interest earned appear instantly.

Does this account for taxes, fees, or contributions?

No. This is a pure compound-interest projection. Real investments involve taxes, fees, inflation, and (for savings goals) periodic contributions — all of which a richer financial-planning calculator would model.

複利計算器 — 終值與複利頻率

複利計算器

FAQs

What is compound interest?: Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. It's the mechanism that makes money grow non-linearly over time — earnings earn earnings.
How is it different from simple interest?: Simple interest is calculated only on the original principal (Interest = P × r × t). Compound interest reinvests each period's interest, so the balance grows at an accelerating rate. Over long horizons the gap is dramatic.
What does compounding frequency change?: It's the number of times per year interest is added to the balance. More frequent compounding produces slightly higher growth at the same nominal rate — but the marginal benefit shrinks fast as frequency increases. Monthly is meaningfully better than annual; daily is barely better than monthly.
What is continuous compounding?: The mathematical limit of compounding infinitely often, given by A = P × e^(r·t) where e ≈ 2.71828. It sets an upper bound on what any other compounding schedule can produce at the same rate.
How do I use this calculator?: Enter the principal (starting amount), the annual interest rate as a percentage, the time in years, and pick a compounding frequency. The final amount and total interest earned appear instantly.
Does this account for taxes, fees, or contributions?: No. This is a pure compound-interest projection. Real investments involve taxes, fees, inflation, and (for savings goals) periodic contributions — all of which a richer financial-planning calculator would model.

什麼是複利？

複利是同時按本金以及之前各期累計利息計算的利息。與只按本金計算的單利不同，複利將每期收益再投資，因此餘額隨時間呈非線性成長。這正是長期儲蓄、退休帳戶和再投資股息能遠遠超過短期線性預測的原因。

複利公式

A = P × (1 + r/n)^n·t

其中 A 為最終金額，P 為本金，r 為年利率（小數形式），n 為每年複利次數，t 為年限。

對於連續複利（n → ∞）：A = P × e^r·t，其中 e ≈ 2.71828。

計算範例

您以年利率 5% 存入 NT$1,000，按月複利，期限 10 年：

A = 1000 × (1 + 0.05/12)^12·10 ≈ NT$1,647.01

獲得利息 NT$647.01。改為連續複利則為 NT$1,648.72，僅多 NT$1.71。

複利頻率

頻率	n（每年期數）	範例：NT$1,000 按 5% 計 10 年
每年	1	NT$1,628.89
每半年	2	NT$1,638.62
每季	4	NT$1,643.62
每月	12	NT$1,647.01
每週	52	NT$1,648.33
每日	365	NT$1,648.66
連續	∞	NT$1,648.72

如何使用本計算器

輸入本金。
輸入年利率（百分比），例如 5 表示 5%。
輸入年限。
選擇複利頻率。
最終金額與利息總額立即顯示。

限制

無定期投入。本計算器僅模擬一次性本金。
未計稅。實際利息收入通常需繳稅。
未計通膨。結果為名目金額。
利率恆定。實際利率會變動。
未計費用。帳戶或基金費用未模擬。

如需個人理財規劃，請諮詢專業財務顧問。