EAR not On your Head

[archived_user]

FV=PV*(1+r/m)^mN
lim as m->∞
FV=PV*(1+r/very large number)^very large number
FV=PV*(1+0)^very large number
1 to the power of anything is still 1.
What is the flaw in my mathematics?
BTW, I have seen:
http://www-stat.wharton.upenn.edu/~waterman/Teaching/IntroMath99/Class04...

 

[archived_user]

Atomic_Sheep wrote: FV=PV*(1+r/m)^mN
lim as m->∞
FV=PV*(1+r/very large number)^very large number
FV=PV*(1+0)^very large number
1 to the power of anything any real number is still 1.
What is the flaw in my mathematics?
BTW, I have seen:
http://www-stat.wharton.upenn.edu/~waterman/Teaching/IntroMath99/Class04...

1^∞ may not be 1; ∞ isn’t a real number.

 

[archived_user]

1 to the power any real number is always one. Also, the value of (r/very large number) is very close to 1 but not equal to it. So, in this case, you would have to use limits (which isn’t covered in the CFA course, so dont worry about it) and the FV value will be equal to:
FV=PV*e^(rN)
which is nothing but the case of continuous compounding.