【簡單利息及複合利息公式】Simple Interest and Compound Interest Formulas

SketchMath 數學團隊 SketchMath Maths Team ｜ 更新 Updated 2026-10-20

簡單利息是 I = Prt，本利和 A = P(1 + rt)。複合利息是利息再生利息：A = P(1 + R%)ⁿ，其中 R% 是每期利率，n 是期數。Simple interest is I = Prt, so the amount is A = P(1 + rt). Compound interest earns interest on the interest: A = P(1 + R%)ⁿ, where R% is the rate per period and n is the number of periods.

用 AI 逐步解簡單利息及複合利息題目 Solve it with AI練習 146 條 DSE 模擬題 Practise 146 DSE-style questions
改變利率 r：直線是 $10 000 的單利，曲線是複利。年期愈長，兩者差距愈大。 Drag the rate r: the straight line is simple interest and the curve is compound interest on $10 000. The gap widens with time. 自己試試 → Try it yourself →

利息公式 Interest Formulas

簡單利息Simple interestI = P × r × t (r per year, t in years)
本利和（單利）Amount (simple)A = P(1 + rt)
本利和（複利）Amount (compound)A = P(1 + R%)ⁿ
複利息Compound interestA − P
每半年／每季計息Half-yearly / quarterly半年計息：R = r/2，n = 2t；每季計息：R = r/4，n = 4tUse R = r/2, n = 2t (half-yearly) or R = r/4, n = 4t (quarterly)
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簡單利息及複合利息例題詳解 Worked Examples

例題 1 Example 1：簡單利息 Simple interest

$10 000 以年利率 5% 單利存款 3 年，求利息及本利和。Find the interest and the amount when $10 000 is deposited for 3 years at 5% p.a. simple interest.

  1. I = 10 000 × 0.05 × 3 = 1500
  2. A = 10 000 + 1500

答案： Answer: 利息 $1500；本利和 $11 500Interest $1500; amount $11 500

例題 2 Example 2：複利（每年計息） Compound interest, yearly

$10 000 以年利率 5% 複利（每年計息）存款 3 年，求複利息。Find the compound interest on $10 000 for 3 years at 5% p.a., compounded yearly.

  1. A = 10 000 × 1.05³ = 11 576.25
  2. 11 576.25 − 10 000

答案： Answer: $1576.25（單利是 $1500）$1576.25 (compare $1500 with simple interest)

例題 3 Example 3：每季計息 Compounded quarterly

$8000 以年利率 6% 按季計息的複利投資 2 年，求本利和。Find the amount when $8000 is invested for 2 years at 6% p.a., compounded quarterly.

  1. 每季利率 6% ÷ 4 = 1.5%；期數 n = 2 × 4 = 8Rate per quarter 6% ÷ 4 = 1.5%; number of quarters n = 2 × 4 = 8
  2. A = 8000 × 1.015⁸ ≈ 9011.94

答案： Answer: $9011.94

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💡 應試陷阱與秘訣 Exam Traps & Secrets

⚠️ 利率與期數要配合 Rate and period must match若每季計息，要把年利率除以 4、年數乘以 4。用 6% 配 n = 8 會令結果偏高。If interest is added every quarter, divide the yearly rate by 4 and multiply the years by 4. Using 6% with n = 8 overstates the amount.
⚠️ 「利息」還是「本利和」？ "Interest" or "amount"?P(1 + R%)ⁿ 是本利和，要減去 P 才是利息。P(1 + R%)ⁿ is the amount. Subtract P to get the interest.
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✏️ 自我測試：互動練習 Self-Test: Interactive Practice

溫習方法：點擊以下任何題目，即時在坐標網格載入並核對計算步驟。How to study: click any question to load it on the coordinate grid and check your steps.

(複利息 Compound interest)$5000 以年利率 3% 複利存款 4 年，求複利息。Find the compound interest on $5000 for 4 years at 3% p.a., compounded yearly.
(求 n Find n)$1000 以年利率 8% 複利計算，最少多少年後超過 $2000？After how many years does $1000 at 8% p.a. compound interest first exceed $2000?
(比較 Compare)比較 $20 000 以年利率 4% 存款 10 年的單利與複利。Compare simple and compound interest on $20 000 at 4% p.a. for 10 years.
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簡單利息及複合利息練習題（DSE 模擬題） Exercises: DSE-Style Practice

SketchMath 題庫內的 DSE 風格練習，選擇題及長題目均附解答。 DSE-style practice from the SketchMath question bank, with solutions for every MC and long question.

百分法（二） · 中三
76 條選擇題 76 MC · 52 條長題目 52 long questions
DSE 溫習：百分法 · 中六
10 條選擇題 10 MC · 8 條長題目 8 long questions

常見問題 Frequently Asked Questions

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