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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?

Respuesta :

YellowGold
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.

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