Here is what
unclemick needs to know.
The mathematics of annuities, bonds and mortgages are all similar for making comparisons. An actual retiree has to plan for the fortunate possibility of living longer than his life expectancy. Insurance companies take advantage of statistics.
Here are the total payments versus the interest rate using the mortgage formula.
Identify the rate for the correct interest rate and number of years and multiply it by the total amount of the mortgage. The product equals the total payment amount, principal plus interest. With bonds and traditional mortgages, all are in nominal dollars. With TIPS and Ibonds, the interest rates and the payment amounts both match inflation.
interest = 0%
20 years: 5.00%
30 years: 3.33%
40 years: 2.50%
interest = 2%
20 years: 6.12%
30 years: 4.46%
40 years: 3.66%
interest = 4%
20 years: 7.36%
30 years: 5.78%
40 years: 5.08%
interest = 6%
20 years: 8.72%
30 years: 7.26%
40 years: 6.65%
The numbers that you have presented come close to matching the payments at a 5% interest rate through one's 80th birthday.
interest = 5%
20 years: 8.02%
30 years: 6.51%
40 years: 5.83%
The insurance company is prepared for unclemick to live a little bit longer. The news is not so good for beachbumz, but it is not especially bad.
This is the formula:
The total payment (which I refer to as the TIPS Equivalent Safe Withdrawal Rate) with an interest rate r over N years can be simplified to: r / [1 - (1 / [1+r]^N ) ] This particular form is good when using a scientific calculator.
The following post has several formulas of this type. From the
3% SWR for 56 Years thread dated Monday, Oct 13, 2003, these formulas come in handy when constructing risk-free baselines.
http://nofeeboards.com/boards/viewtopic ... 536#p12536
This is what you need to know mathematically. What you can withdraw as an individual is limited by an uncertain lifespan (suicide is no solution). You can calculate the advantage that you get because an insurance company charges based on statistical averages, not individuals.
Have fun.
John R.