if you can understand the 'concept' of an E-Bar, I firmly believe you are well over 90% of the way there. this is how I explain it (I have an old powerpoint from an asppa presentation I did so it wasn't hard to copy this info) Bob, age 60, receives a $44,000 contribution. He makes $220,000 a year. Not bad, 20% of pay. What is his E-BAR? Using an interest rate of 8.5%, what will that 44,000 grow to at retirement age? • Age 61 = 44,000 * 1.085 = 47,740 • Age 62 = 47,740 * 1.085 = 51,798 • Age 63 = 51,798 * 1.085 = 56,201 • Age 64 = 56,201 * 1.085 = 60,978 • Age 65 = 60,978 * 1.085 = 66,161 66,161 is the lump sum or future value. So at retirement he will have over $66,000 Mathematically speaking, this could be written as 44,000 * (1.085)^5 • Or, generically speaking (contribution * interest assumption for however many years to retirement remain) n*(1.0I ) yrs to retirement where n= contribution I = interest assumption (must between 7.5% and 8.5%) The APR for 1983 IAF at 8.5% interest is 115.39 you might see this expressed as 9.6158. The first figure is for monthly annuity, the second figure is annual (Depending on which mortality table is chosen the rate will be different, but in most cases it becomes a constant across the board so don't worry about that) • Balance = $66,161 • To translate this to a benefit, simply divide by the APR (Annuity Purchase Rate) • 66,161 / 115.39 = $573.37 a month [monthly benefit] • Or, an annual amount of 12 * 573.37 = 6880.44 So what percentage of pay is that? • 6880.44 / 220,000 = 3.127%
• Congratulations. You have just calculated an E-BAR!!!! • In other words, a one-time total contribution of $44,000 (20% of pay) to this individual at age 60 will provide an annual benefit of 3.127% of pay for life at age 65.
[if you tell me you understand that concept, then you can go to the next step (at least in my opinion) as to why new comparability works]