I wish to solve an equation for my friend. Can someone let me know the solution step by step?
3.79 = [(1+r)^5 - 1]/(1+r)^5
I wish to derive vale of r. If possible please generalize the polynomial equation to nth exponent.
Thanks,
Ravi
I wish to solve an equation for my friend. Can someone let me know the solution step by step?
3.79 = [(1+r)^5 - 1]/(1+r)^5
I wish to derive vale of r. If possible please generalize the polynomial equation to nth exponent.
Thanks,
Ravi
The first thing I would do is let y= 1+ r so the equation becomes the slightly simpler [tex]3.79= \frac{y^5- 1}{y^5}$\displaystyle . So $\displaystyle 3.79y^5= y^5- 1$, $\displaystyle 2.79y^5= -1$, and $\displaystyle y^5= \frac{-1}{2.79}= -0.3584$ (approximately). $\displaystyle y= \sqrt[5]{-0.3584}$. That has one real and five complex roots. Once you have found y, of course, r= y- 1.
Generalizing to $\displaystyle 3.79= \frac{(1+r)^n- 1}{(1+ r)^n}$, letting y= 1+ r, that becomes $\displaystyle 3.79= \frac{y^n- 1}{y^ n}$. So 3.79y^n= y^n- 1$. $\displaystyle 2.79y^n= -1$. [tex]y^n= -\frac{1}{2.79}= -0.358. $\displaystyle y= \sqrt[n]{-\frac{1}{0.358}}$.
If n is odd, that has one real root. If n is even there is no real root. In either case, there are n complex roots.
Yes, there is an error. It is financial formula. My friend told it is some interest rate calculation formula.
Apologize, it should have been -
3.79 =[(1+r)^5 - 1]/r(1+r)^5
If some one could answer it, it should definitely help.
Well, tell your friend to stay out of the banking business!
Equation looks wrong again; is it:
3.79 =[(1+r)^5 - 1] / [r(1+r)^5] ?
If so, then r = .1
IF it is as you posted, then r = -.039
Still makes no sense...WHAT is the formula intended for?
To calculate the rate required for 1 dollar
to grow to 3.79 over 5 years?