# Thread: Interest rate calculation

1. ## Interest rate calculation

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

2. ## Re: Interest rate calculation

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} $. So img.top {vertical-align:15%;} $3.79y^5= y^5- 1$, $2.79y^5= -1$, and $y^5= \frac{-1}{2.79}= -0.3584$ (approximately). $y= \sqrt[5]{-0.3584}$. That has one real and five complex roots. Once you have found y, of course, r= y- 1.

Generalizing to $3.79= \frac{(1+r)^n- 1}{(1+ r)^n}$, letting y= 1+ r, that becomes $3.79= \frac{y^n- 1}{y^ n}$. So 3.79y^n= y^n- 1" alt=". So $3.79y^5= y^5- 1$, $2.79y^5= -1$, and $y^5= \frac{-1}{2.79}= -0.3584$ (approximately). $y= \sqrt[5]{-0.3584}$. That has one real and five complex roots. Once you have found y, of course, r= y- 1.

Generalizing to $3.79= \frac{(1+r)^n- 1}{(1+ r)^n}$, letting y= 1+ r, that becomes $3.79= \frac{y^n- 1}{y^ n}$. So 3.79y^n= y^n- 1" />. $2.79y^n= -1$. [tex]y^n= -\frac{1}{2.79}= -0.358. $y= \sqrt[n]{-\frac{1}{0.358}}$.

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.

3. ## Re: Interest rate calculation

Originally Posted by RaviT
3.79 = [(1+r)^5 - 1]/(1+r)^5
As equation is shown, r = -1.81448...

Looks like some financial formula, where r = interest rate.
However, I have a feeling your equation is wrong: typo?

4. ## Re: Interest rate calculation

Thank you so much ! This helps.

5. ## Re: Interest rate calculation

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.

6. ## Re: Interest rate calculation

Originally Posted by RaviT
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
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?