In other words, investing at 11% a year continuously compounded is exactly the same as investing at...

1. Suppose you invest $1 at a continuously compounded rate of 11% ( r = .11) for one year ( t =1). The end-year value is e .11 , or $1.116. In other words, investing at 11% a year continuously compounded is exactly the same as investing at 11.6% a year annually compounded.

2. Suppose you invest $1 at a continuously compounded rate of 11% ( r = .11) for two years ( t = 2). The final value of the investment is e ^rt = e .22 , or $1.246. Sometimes it may be more reasonable to assume that the cash flows from a project are spread evenly over the year rather than occurring at the year’s end. It is easy to adapt our previous formulas to handle this. For example, suppose that we wish to compute the present value of a perpetuity of C dollars a year. We already know that if the payment is made at the end of the year, we divide the payment by the annually compounded rate of r:

PV =C/r

If the same total payment is made in an even stream throughout the year, we use the same formula but substitute the continuously compounded rate.