The US Social Security system provides workers with the option of retiring at age 62 and having a lower social security benefit or waiting until age 66 (or later depending on your birth year) and receiving their full benefits. This year, somebody retiring at age 62 would receive $25,200 per year whereas somebody who turns 66 this year would receive $33,600 per year. Each year, the benefit levels increase with inflation. In other words, if somebody is currently age 62 and starts taking benefits, next years income will be $25,200 increased by one year of inflation.

a. You are advising a family friend who is about to turn 62 on whether they should start receiving benefits now or wait until age 66. Assume that the appropriate discount rate is 5%, inflation is expected to be 2.2% per year for the foreseeable future, and that the person you are advising expects to live until age 83. Assuming no changes to the program, would it be more valuable to wait until age 66 or start receiving benefits now?

b.Policymakers are concerned about the long-term viability of Social Security and are considering dramatic changes to the program. The Social Security system currently raises $920 billion per year in income and pays $800 billion per year in benefits. However, with the pending retirement of the Baby Boom generation, benefits levels are expected to increase at the rate of 3.7% per year (2.2% inflation plus 1.5% annual increase in the number of beneficiaries) whereas income (FICA taxes) is expected to grow only 2.2% per year (inflation) as the workforce is not forecast to grow. Continue to assume that the appropriate discount rate is 5%. Using a 75 year forecast time period (as used by policymakers), estimate the solvency of the Social Security system. In other words, what is the value of its expected payments relative to its expected tax revenues at the end of 2016 (beginning of 2017)? Please show excel formulas. Thanks!