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10 August, 12:16

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?

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  1. 10 August, 12:26
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    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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