If you deposit P dollars in a retirement fund every year for N years with the intention of then withdrawing Q dollars per year for M years, you must earn interest at a rate r satisfying

Assume that $2000 is deposited each year for 30 years and the goal is to withdraw $10,000 per year for 25 years. Use Newton’s Method to compute b and then find r. Note that b = 1 is a root, but you want the root satisfying b > 1.

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P(bN 1) = Q(1-b-M), where b= 1 + r