Your friends Greg and Ellen have come to you for some help after hearing how well you did in your finance class. Greg and Ellen are both 60 years old, plan to retire at age 62, and are wondering when to take Social Security. Greg and Ellen have saved $850,000 for retirement and expect that to grow to $925,000 at age 62. They will have no other sources of income in retirement other than Social Security and their retirement savings. Greg and Ellen reach full retirement age for Social Security purposes at age 66. The earliest they can take Social Security is age 62, and the latest is age 70. They each receive a $2,100 monthly benefit at full retirement age. If they take Social Security at age 62, their benefit monthly benefit will be reduced by 25%. If they delay Social Security until age 70, their monthly benefit will grow 8% for each year they delay benefits after age 66. Greg and Ellen have worked out an annual retirement budget of $60,000 in today's dollars. Assume that the cost-of-living adjustment for SS is 2% annually, and that living expenses increase at a 2.5% inflation rate. After age 62, Greg and Ellen believe they can earn a 6% return on their retirement nest egg. Gregs family health history suggests he will live to age 85, and Ellen's history suggests she will live until age 90. Use these ages for the purpose of your analysis. If they want to maximize the inheritance they leave to their son Max and daughter Ruby, at what age should they take Social Security? (Assume that they will have to use their retirement nest egg to make up whatever income shortfall there is.) What age do Greg and Ellen have to reach so that the decision to wait until full retirement age (66) is more beneficial than taking Social Security at age 62? (Hint: Think break-even analysis.)