May 15

Compound Frequency - 9 min. screencast

by David Harper, CFA, FRM, CIPM

FRM |

image

Here are the key formulas that relate continuous compounding to discrete compounding:

compound_frequency

 

The example I use in this screencast is $100 (initial value = A = $100) and a one year period (n = 1).

The idea is simply to show

  • Increasing the compound frequency increases the terminal (end of year) value ("putting the money to work harder") until we get to the ultimate in frequency: continuous = ($100)EXP[(rate)(time)]
  • We can work backwards, from the continuous rate of return (see middle orange column, matches orange formula above). Every discrete compound frequency can be translated from the continuous frequency
  • In blue, merely the "proof" that the various discrete rates all produce the same result

 

compound_freq_2

Here is the screencast:

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