In Section we had established an association among the effective and nominal rate of interest where compounding arise n times a year that is as given:

r = (1 +  k/m )^m - 1

Rearranging equation a10, this can be specified as:

r = [(1 +  k/(m/k))^m/k ]^k- 1

Let us substitute m/k by x from Eq (a11)

r = [(1 + 1/x )^k] - 1

In continuous compounding ∞ → m that implies ∞ →∞  in Eq 12.

= e = 2.71828...

By equation (a12) results in

R = e^k-1

⇒ (r + 1) =  e^k

Thus the future value of an amount when continuous compounding is done is as follows:

 FV_n = PV * e^km