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More than two decades ago, Bill Bengen, then a financial planner in Southern California, said he had several anxious clients with the same question: How much can I spend in retirement without running out of money?

Being relatively new to the profession, he dived back into his finance textbooks for answers, but said he couldn’t find any guidelines rooted in facts. “I decided to get down to business with my computer,” said Mr. Bengen, 67, who retired in 2013 and now lives with his wife in La Quinta, a resort town in California’s Coachella Valley.