# Math Help - Infinite and Geometric Series: Continuously Compounded Interest

1. ## Infinite and Geometric Series: Continuously Compounded Interest

I can't figure out how to set up an appropriate series for this problem.

"Set up an appropriate (series) model to answer the given question."

"How much should you invest today at an annual interest rate of 15% compounded continuously so that, starting next year, you can make annual withdrawals of \$2000 forever?"

Looking at it algebraically, the minimum you could invest would be 12,358.33. But I can't figure out how to set the problem up as a convergent series. An explanation of how to do so would be greatly appreciated.

Edit: I think the better way to put my question is: This is a "trick" question, right? There is no way to solve this problem using a series because any series that one sets up to model the problem is going to diverge. Assuming that the starting sum has to be in terms of round dollars and cents, the minimum starting balance is slightly more that is absolutely necessary. Each year, a bit more interest is earned than is needed to pay out the 2,000 dollars. Therefore, the principle grows without bound. (Or, if one assumes that the earned interest is rounded off to the nearest penny every year, the ballance remains static.) If this is the case, I just need someone to reinforce my thinking. Of course, if I am completely missing the solution, please let me know!

Edit: I asked my teacher, and she showed me the correct series -- it does exist!