利率換算器

分類： Uncategorized
- August 31, 2026
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Convert between Annual Percentage Rate (APR) and Effective Annual Rate (EAR) to understand the true cost of loans and investments

Rate Conversion

%
Effective Annual Rate (EAR)
5.12%
The true annual return accounting for compounding
%
Annual Percentage Rate (APR)
4.89%
The nominal annual rate without compounding

Comparison

APR vs. EAR over Different Compounding Frequencies

APR to EAR Conversion Table

Compounding APR: 5.00% Effective Rate Difference

Conversion Formulas

APR to EAR Formula:

EAR = (1 + APR/n)n - 1

Where n is the number of compounding periods per year. For continuous compounding, the formula is: EAR = eAPR - 1

EAR to APR Formula:

APR = n × ((1 + EAR)1/n - 1)

Where n is the number of compounding periods per year. For continuous compounding, the formula is: APR = ln(1 + EAR)

Understanding Interest Rate Conversions

When analyzing loans, investments, or financial products, understanding the difference between APR and EAR is crucial for making informed decisions. These rates may seem similar, but they represent interest in fundamentally different ways.

Annual Percentage Rate (APR)

  • Simple interest rate: Does not account for compounding
  • Nominal rate: The stated interest rate without considering frequency of compounding
  • Required for loans: In many countries, lenders must disclose APR by law
  • Linear calculation: Easy to calculate but doesn't show the true cost over time

Effective Annual Rate (EAR)

  • Compound interest rate: Accounts for the effects of compounding
  • True annual cost: Reflects the actual amount paid/earned over a year
  • Comparison tool: Allows accurate comparison between different compounding frequencies
  • Always higher: EAR is always higher than APR (except for annual compounding)

Practical Examples

Credit Card Example

A credit card with 18% APR compounded monthly has an EAR of 19.56%. This means you'll actually pay 19.56% interest over a year if you don't pay your balance in full each month.

Savings Account Example

A savings account offering 2% APR with daily compounding has an EAR of 2.02%. The difference is small but becomes more significant with higher interest rates or longer time periods.

Investment Example

An investment promising 8% APR compounded quarterly has an EAR of 8.24%. When comparing investments, using EAR provides a more accurate picture of your actual returns.

本工具計算什麼

名義利率、實際年利率與連續複利之間的換算。

公式
實際年利率 =（1 + 名義利率 ÷ n）ⁿ − 1；連續複利 = e^r − 1
計算示例
名義利率 6%、按月複利，實際年利率為（1 + 0.06/12）¹² − 1 = 6.17%。
何時使用
比較以不同複利方式報價的利率時使用。
常見錯誤
直接將按月複利與按年利率比較。表面數字接近，實際年利率卻不同。