(1) PV := C ( 1/r - e^(-nr)/r ) where r is the "continuous" interest
rate
This is supposed to represent an amount C every year for n years,
distributed uniformly through the year.
The thing is this: if I try to do an analogy with a given "partition" of
the
year, resulting in an amount C taken m times a year (and an interest rate
capitalized m times a year), the formula would then be:
(2) PV := (C/m) ( 1/r - (1+r)^(-nm)/r) r is the interest rate
capitalized
m times a year
Note that e^(-nr) in (1) is equivalent to (1+r)^(-nm) in (2); 1/r prevails
in both formulas.
So the amounts actually given are C/m, totalizing C in a year term. What
annoys me is that(1) doesn't divides C by m... shouldn't there be any
adjustment to C in order to reflect the *uniform partitioning* of the
payment?? I know there must be something wrong with my reasoning, but I
need
to know what it is.
Any comments would be greatly appreciated.
Fernando