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Effective Interest Rate (EAR) Calculator

Enter a nominal annual rate and how often interest compounds (annually, semiannually, quarterly, monthly, or daily) to instantly get the effective annual rate (EAR). See how it differs from the nominal rate and the annual interest gap on a given principal.

Input

%
Compounding frequency (times per year)
× 10,000

Result

Effective annual rate (EAR, Monthly)

5.11619%

Nominal annual rate

5 %

Compounding periods per year

12

Annual interest difference on $1,000,000.00

+$1,161.90

How it works

  • The effective annual rate (EAR) is found by dividing the nominal annual rate by the number of compounding periods m, adding 1, raising the result to the power of m, and subtracting 1: EAR = (1 + nominal rate ÷ m)^m − 1.
  • The compounding count m depends on the frequency: annually = 1, semiannually = 2, quarterly = 4, monthly = 12, and daily = 365. The more often interest compounds, the more the effective rate exceeds the nominal rate.
  • When compounding is annual, m = 1 and the effective rate equals the nominal rate (annual compounding is the base case).
  • Enter a principal and the calculator finds the yearly interest under simple interest (principal × nominal rate) and under the effective rate (principal × EAR), then shows the difference as the annual interest gap.
  • It also supports the reverse: deriving the nominal rate required to reach a target effective rate, using nominal rate = m × ((1 + EAR)^(1/m) − 1). Rates are shown to about six decimal places.
  • Note: results are estimates based on compound-interest math. Real savings, loans, and investments may yield differently due to fees, taxes, day-count conventions, and rate changes.