?Retirement Savings Designed by Bill Bengen, the 4 percent rule says that a retiree may

Chapter 10, Problem 41

(choose chapter or problem)

Retirement Savings Designed by Bill Bengen, the 4 percent rule says that a retiree may withdraw 4% of savings during the first year of retirement, and then each year after that withdraw the same amount plus an adjustment for inflation. Under this rule, your retirement savings should be expected to last 30 years, which is longer than most retirements.

(a) If your retirement savings is $750,000, how much may you withdraw in your first year of retirement if you want the retirement savings to last 30 years?

(b) According to the American College of Financial Services, the proportion of people 60 to 75 years of age who believe it would be safe to withdraw 6 to 8 percent of their retirement savings annually is 0.16. Suppose you conduct a survey of twenty 60 to 75 year olds and ask them if it is safe to withdraw 6 to 8 percent of retirement savings annually if they wish their retirement savings to last 30 years. Explain why this is a binomial experiment. What are the values of n and p?

(c) In a random sample of twenty 60 to 75 year olds, what is the probability exactly 8 individuals will believe it is safe to withdraw 6 to 8 percent of retirement savings annually if they wish their retirement savings to last 30 years.

(d) In a random sample of twenty 60 to 75 year olds, what is the probability fewer than 8 individuals will believe it is safe to withdraw 6 to 8 percent of retirement savings annually if they

wish their retirement savings to last 30 years.

(e) Suppose you obtain a random sample of five hundred 60 to 75 year olds. Explain why the normal model may be used to describe the sampling distribution of pn the sample proportion of 60 to 75 year olds who believe it is safe to withdraw 6 to 8 percent of their retirement savings annually. Describe this sampling distribution. That is, find the shape, center, and spread of the sampling distribution of the sample proportion.

(f) Use the normal model from part (e) to approximate the probability of obtaining a random sample of at least one hundred 60 to 75 years olds who believe it would be safe to withdraw 6 to 8 percent of their retirement savings annually assuming the true proportion is 0.16. Is this result unusual? Explain.