Continous Compounding Derivation

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Atomic_Sheep

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The formula for
FV = PV * (1 + rs/m) ^ mN
as m -> 8(infinity)
rs/m -> 0
&
mN -> 8 (infinity)
We then get:
FV = PV * (1 + 0) ^ 8
which equals
FV = PV * 1
FV =PV
Obviously wrong… however I can’t figure out where my mistake is…
 
Atomic_Sheep wrote:
The formula for
FV = PV * (1 + rs/m) ^ mN
as m -> 8(infinity)
rs/m -> 0
&
mN -> 8 (infinity)
We then get:
FV = PV * (1 + 0) ^ 8 ∞
which equals
FV = PV * 1
FV =PV
Obviously wrong… however I can’t figure out where my mistake is…
Click to expand...
There it is.
 
I was using 8 to denote infinity…
Thanks JSD-NYC… wow was way off… my maths isn’t good enough to derive that in an exam environment :( seems I’ll just have to commit it to memory.
 
1^∞ is not necessarily 1.
Technically, 1^∞ is known as an indeterminate form. Other indeterminate forms are:
0 / 0, ∞ / ∞, 0^0, and ∞ − ∞.
All of these require calculus to evaluate.
 
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