Today, you are retiring. you have a total of $289,416 in your retirement savings. you want to withdraw $2,500 at the beginning of every month, starting today and expect to earn 4.6 percent, compounded monthly. how long will it be until you run out of money?

The answer is 17 years and 6 months.

Let P=$289,416, A=$2,500, r=0.046 (4.6%), m=12 (monthly compounding) where i = r/m, and n be the time until you run out of money. Then, i=0.046/12 = 0.038333.Using the equation P = A + A{[1-(1+i)^(1-mn)]/i}, we can derive an equation for n.
Therefore, n = (1/m)*{1-[(log(1-(i*(P-A)/A)))/log(1+i)]}. This will give n = 17.516 years or approximately 17 years and 6 months.

Answermediation;

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