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 2008 mathestate Fri 19 Dec 2008