Financial

Equivalent Rate Calculator

Convert interest rates between different periods (annual, monthly, daily) using the financial equivalence formula. Compare investments and understand the real cost of financing.

When to Use

  • • Compare the profitability of investments over different periods
  • • Calculate the monthly rate of an annual loan
  • • Convert interest rates for analysis
  • • Understand the real cost of financing

Related Tools

Also use the Compound Interest Calculator and the Simple Interest Calculatorfor complete analyses

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What is an Equivalent Rate?

An equivalent rate is one that, when applied over different periods, produces the same financial result at the end of a year. For example, a rate of 12% per year is not equivalent to 1% per month, as compound interest accumulates exponentially.

The conversion uses the mathematical formula: (1 + i_original)^(n_original) = (1 + i_destination)^(n_destination), where n is the number of periods in a year.

Conversion Formula

Introduction to the formula

Formula 1

Formula 2

Legend

Conclusion

Difference Between Proportional and Equivalent Rate

Introduction to section 3

Original RateAnnual EquivalentMonthly EquivalentDaily Equivalent
18% ao ano18,00%1,3888%0,0454%
1,2% ao mês15,3895%1,20%0,0392%
0,08% ao dia (365 dias)33,8947%2,4622%0,08%

Practical Applications

  • Compare CDs with annual profitability vs. monthly savings
  • Calculate the real monthly cost of an annual loan
  • Analyze investment funds with different periods
  • Convert credit card rates (monthly to annual)

Frequently Asked Questions about Equivalent Rate

Click to expand and see direct answers with practical examples.

What is the difference between equivalent rate and proportional rate?+

A proportional rate is a simple division (e.g., 12% per year ÷ 12 = 1% per month). An equivalent rate considers compound interest and is mathematically accurate. For real investments, always use the equivalent rate.

How to convert 1% per month to an annual rate?+

Use the formula: (1 + 0.01)^12 - 1 = 0.1268 or 12.68% per year. Note that it is not simply 1% × 12 = 12%, as compound interest accumulates.

Why is 12% per year not equal to 1% per month?+

Because compound interest accumulates exponentially. 12% per year is equivalent to approximately 0.9489% per month. If you apply 1% per month for 12 months, the result will be 12.68% per year.

When to use a base of 360 or 365 days?+

Banks generally use 360 days (commercial year) to simplify calculations. More accurate investments and financial analyses use 365 days (civil year). Our calculator allows you to choose.

Can I use the equivalent rate to compare investments?+

Yes! It is the correct way to compare. Convert all rates to the same period (monthly or annual) using the equivalent rate, then compare the values. Never use proportional rates for comparison.