Suppose that Alan goes to work at age 22, earns on average $60,000 a year for 43 years, and inherits $300,000 the year he starts working. He expects to live to be 82.
(a) Calculate on average how much Alan consumes per year, the ratio of his annual consumption to annual income, and his savings rate.
(b) Suppose that a rise in housing prices causes Alan’s inheritance to increase to $480,000. If Alan does not change his retirement age, calculate Alan’s new annual consumption, as well as the new ratio of annual consumption to annual income, and his annual savings rate.
(c) Given the increase in his inheritance listed in part b, suppose that Alan decides to use the increased inheritance to finance an earlier retirement age. He does this by maintaining the same average annual consumption as in part a. At what age will Alan be able to retire?