Solve for N..

I cannot see any DIRECT solution for N. There maybe a way but I cannot see it. However, using the method of iteration and interpolation, it gives a value for N =5.36064361355.

I have checked it by substituting it into the equation, and it balances the equation to the penny.

Good luck to you.

[10,000*1.05^N]+[15,000*1.06^N]+[20,000*1.07^N]+[25,000*1.08^N]=100,000

\([10,000*1.05^N]+[15,000*1.06^N]+[20,000*1.07^N]+[25,000*1.08^N]=100,000\\ [1.05^N]+[1.5*1.06^N]+[2*1.07^N]+[2.5*1.08^N]=10\\\)

Answer from Wolfram|Alpha                Just as guest#1 said. :)

https://www.wolframalpha.com/input/?i=%5B1.05%5EN%5D%2B%5B1.5*1.06%5EN%5D%2B%5B2*1.07%5EN%5D%2B%5B2.5*1.08%5EN%5D%3D10