Need to know HOW to solve(have correct answer+equation)

Hi; I am honestly unsure as to which forum this belongs in so I'll put it here and if it needs to be moved it can be moved. Anyways, this is for a finance class

**QUESTION**

After saving diligently your entire career, you and your spouse are ready to retire with a nest egg of $600,000. You need to invest this money in a mix of stocks and bonds that will allow you to earn $5,000 per month for 30 years. What annual interest rate (APR) do you need to earn?

**ANSWER**

9.4% = i

**SET-UP**

600,000 = 5,000 * [ ( 1 - (1 / (1+i)^360) ) / i ]

I am getting stuck on how you break down the equation in steps to solve for i. Can somebody please show me how it is done?

NOTE: I am not asking you to plug .094 in for i; I am simply asking how you SOLVE for it. Thank you for any help!

Re: Need to know HOW to solve(have correct answer+equation)

So your equation is $\displaystyle 600000= 5000\frac{1- \frac{1}{(1+ i)^{360}}}{i}$?

The first thing I would do is divide both sides by 5000i

$\displaystyle 120i= 1- \frac{1}{(1+i)^{360}}= 0$

I think I would be inclined to let x= 1+ i so that i= x- 1: the equation becomes

$\displaystyle 120(x- 1)= 120x- 120= 1- \frac{1}{x^{360}}$

Multiplying both sides by $\displaystyle x^{360}$, $\displaystyle 120x^{361}- 120x^{360}+ 1= 0$

A rather nasty polynomial equation!

Re: Need to know HOW to solve(have correct answer+equation)

Thank you for helping me with this