Compound Frequency & EAR Calculator
From the nominal annual rate and compounding frequency, compute the effective annual rate (EAR) and the final amount.
輸入資料
計算結果
重點速覽：EAR = (1 + r/m)^m - 1; final = principal x (1 + r/m)^(m·n). More frequent compounding lifts the real rate, approaching the continuous limit e^r - 1. Example: 5% nominal monthly → EAR ≈ 5.12%, HK$100k for 10y ≈ HK$164,701. WARNING: Quotes differ (APR vs EAR); compare on EAR. Education, not advice.
計算公式
EAR = (1 + r/m)^m − 1。
期末 = 本金 × (1 + r/m)^(m×n)。
連續複利極限 EAR = e^r − 1。
使用說明
- Enter the principal.
- Enter the nominal annual rate and compounding frequency.
- Enter the years to see EAR and the final amount.
理財情境案例
10 萬、5%、月複利、10 年
EAR = (1 + 0.05/12)^12 − 1 ≈ 5.12%。
期末 = 100,000 × 1.0041667^120 ≈ 164,701。
常見問題
What is the difference between EAR and APR?
APR is the nominal rate ignoring compounding frequency; EAR includes compounding and reflects the true annual return/cost. Compare products on EAR.
Is more frequent compounding always better?
For deposits, yes (more return); for loans, it means higher cost. But the marginal gain shrinks — monthly vs daily is tiny, both near the continuous limit e^r - 1.
Why isn't daily compounding infinite?
Because it converges to the mathematical cap e^r - 1. At 5%, continuous ≈ 5.127%; daily 5.126% is already very close.
Can I use this for loan cost?
Yes. A loan's nominal rate compounded monthly has a higher true cost (EAR). Compare loans on EAR, especially across different compounding frequencies.
What does Hong Kong disclosure use?
Hong Kong loan rules often require APR disclosure (including fees); deposits are usually quoted APR. For a fair comparison, look at EAR — this tool converts it for you.
相關工具
參考資料
內容審核：香港計算器科學團隊。EAR 公式與極限驗證。