Request for Question Clarification by
mathtalk-ga
on
06 Mar 2004 06:27 PST
Of the other three quantities besides C, the only one which can be
easily solved for is VA:
VA = C * (1 - (1+i)^-n)/i
While one can explicitly solve for n, the formula cannot guarantee an
integer value of n. In practice this corresponds to a payment
schedule in which the size of the final payment is smaller than the
equal sized payments that make of the rest of the schedule. So some
additional rules are needed, unless you'd be satisfied with simply
getting values of n that aren't whole numbers.
Finally a solution for i in terms of VA, C, and n cannot be
"explicitly" formulated except in special cases, e.g. small values of
n. To see why, let:
r = VA/C
and multiply both sides of:
r = (1 - (1+i)^-n)/i
by i * (1+i)^n. Then for a whole number n:
r * i * (1+i)^n = (1+i)^n - 1
would be a polynomial equation for i of degree n+1, and in general it
must be solved by "iterative" methods instead of an explicit formula.
One might also treat mathematically the solution for n not a whole
number, but I'm doubtful what significance this would have for your
intended application.
Since your interest is in programming to generate i and the other
values, this is scarcely a "show stopper", but it may explain why your
Question has not been answered yet, esp. in view of an offered price
that is normally associated with Questions that can be answered in a
single link or paragraph. Yours is a three part Question whose parts
are of varying difficulty or "messiness".
regards, mathtalk-ga