The US Social Security system provides workers with the option of retiring at age 62 and having a lower monthly social security benefit or waiting until age 67 and receiving their full benefits. This year, somebody retiring at age 62 would receive $2,364 per month whereas somebody who turns 67 this year would receive $3,345 per month. Each year, the benefit levels increase with inflation. In other words, if somebody is currently age 62 and starts taking benefits now, next years monthly income will be $2,364 increased by one year of inflation. If the 62-year-old waits until age 67 to retire, their first-year benefits would be higher than $3,345 by five years of inflation.

Q: You are advising a family friend who is about to turn 62 on whether they should start receiving benefits now or wait until age 67. Assume that the appropriate discount rate is 4.5%, inflation is expected to be 2.5% per year for the foreseeable future, and that the person you are advising expects to live until age 85 (assume they die right before their 85^th birthday, meaning they would receive 23 or 18 years of payments). Assuming no changes to the program, would it be more valuable to wait until age 67 or start receiving benefits now? Evaluate on an annual basis (ignore within year compounding).