Financial Returns

We begin an investigation of financial returns with a very simple model, that of compound interest.  A starting principal is which grows at constant annual decimal rate, ar, with interest compounded each year.  The resulting formula, has time, t, in years.

More typically for a savings account, the compounding interval might be daily with the formula becoming:

The compounding interval can be made infinitely small leading to the formula for continuous interest.  r is now a continuous interest rate.

To convert an annual decimal rate to a continuous rate, where log is the natural logarithm (the conversion will then give the same result as the first equation to the continuous equation):

r = log(1 + ar)

The effective annual rate of the daily compounding is actually:

0.072501 Annual Rate

0.0699933 Continuous Rate

© Copyright 2007 mathestate    Fri 14 Dec 2007