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The Effective Annual Interest Rate

Posted on January 22, 2021January 22, 2021 by financialeducation

We described an interest rate (r) is the rate of return that equates the value of different cash flows on different dates.

If you could pay $975 today to receive $1,000 in 1 year, you can consider the value of waiting 1 year to be $25 ($1,000 – $975.) It can be expressed as an interest rate, r = 25/975 = 0.02564 or 2.56%.

In many cases, interest is paid more frequently than annually. In such cases the future value formula can be expressed as:
FVN = PV(1+rs/m)^mN
where m is the number of compounding periods and N is the number of years.

Interest can also be compounded continuously, in which case FVN = PVersN where e is the transcendental number e = 2.718… Most financial calculators have a function for ex.

Consider a stated interest rate of 6% annually. For different compounding periods, the effective annual interest rate the investor would earn is summarized below.

mmNrs/mFuture value per $
Annual16%/1 = 6%1(1.06) = 1.06
Semiannual26%/2 = 3%1(1.03)2 = 1.0609
Quarterly46%/4 = 1.5%1(1.015)4 = 1.0614
Monthly126%/12 = 0.5%1(1.005)12 = 1.0616
Daily3656%/365 = 0.0164%1(1.0000164)365 = 1.0618
Continuous1e0.06 = 1.06184

The more frequently a given rate is compounded, the higher the ending value for the investor.

2 thoughts on “The Effective Annual Interest Rate”

  1. Pingback: Future and Present Values of Money - Financial Education
  2. Pingback: The Time Value of Money - Financial Education

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