EAR not On your Head

CFA Level I Quant
#1

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/Notes/node13.htm

#2

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

#3

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.

#4

Ok thanks.

#5

I believe that I already wrote that.

There. That’s better.