f=((((1+r)^n)-1)/r)c. I can't solve this for r

Question

f = c  (1+r)ⁿ -1

.           r

 

A description of the formula is here:

 

https://www.investopedia.com/walkthrough/corporate-finance/3/discounted-cash-flow/annuities.aspx

 

I'm trying to solve for "r" which would calculate the rate of return required given a set regular payment (c) to reach the desired future value (f).

 

I'm stuck!

 

Any help would be greatly appreciated.

 

James

 

Answer 1

Hello James,

For the equation

f = c * [(1 + r)ⁿ - 1] / r, multiply both sides by r,

 

→ fr = c * [(1 + r)ⁿ - 1]. Divide both side by c

 

→ fr / c = (1 + r)ⁿ - 1. Add 1 to both sides

→ fr / c + 1 = (1 + r)ⁿ. Take the n'th root of both sides

→ ⁿ√[fr / c + 1] = ⁿ√[(1 + r)ⁿ]. This will clear the radical on the right side, leaving just what is inside

→ ⁿ√[fr / c + 1] = 1 + r. Subtract 1 from both side, and you have 'r' alone

→ r = ⁿ√[fr / c + 1] - 1.

 

Thank you for the question. If you message me directly, I can provide a better formatted version.

 

Kind regards,

Michael E.