Solve for r: V=A*((1+r)^n-1)/r ?

Question

Can this be solved for r symbollically?

V=A*((1+r)^n-1)/r

................(1+r)^n - 1.......................
V= A * ----------------------
.......................r...............................

Answer 1

In terms of r, this is a transcendental equation. You cannot separate r algebraically. Given values for the other variables you can find r numerically by iteration.

Answer 2

................(1+r)^n - 1.......................
V= A * ----------------------
.......................r.........

We may rewrite this equation to look like this:

V = A { [(1+r)ⁿ - 1] / r }
_______________________________________
DIVIDING by "A" we get:

V = A { [(1+r)ⁿ - 1] / r }
V/A = ( A { [(1+r)ⁿ - 1] / r } ) / A
V/A = [(1+r)ⁿ - 1] / r
_________________________________

Breaking the NUMERATOR into two FRACTIONS we get:

V/A = [(1+r)ⁿ - 1] / r
V/A = { [(1+r)ⁿ] / r } - (1/r)

V/A = { [(1+r)ⁿ] / r } - (1/r)
V/A = { [(1+r)ⁿ] / r } - r ֿ¹

.........Well, that's as far as I got, tonight.

I'll keep work'n on it!

I will ask some colleges of mine about this, at work!

It does not seem like we can ISOLATE the variable "r" algebraically.

Good Luck! :o)

Answer 3

I have used webmath to answer all of my equation questions. Webmath allows you to insert your own equations and shows you how the answer was obtained. You can go to the Algebra section and enter the problem under "Simplifying Espressions" and click on "Anything Else". This will help you throughout your math course and you will not have to wait for answers.