Life Annuities

Suppose your age is A and you have \$D in your pocket and you want to buy a Life Annuity with this money, the monthly payments to start immediately and end when you drop dead ... or maybe the payments are transferred to your spouse when you die ... and maybe you want umpteen years of payments guaranteed, even if you drop dead immediately.

The insurance company has to determine how long you'll live (they use mortality tables) whether you're male or female (the tables are different), how long your spouse will live (if the payments pass to the survivor) and what return they can get by investing the \$D (the payments will depend upon a long term bond rate) and how much they want to keep and how much they want to give you, monthly ...

Alas ... so many factors ... aah, but we can provide a rough (sometimes quite rough) estimate like so:

We invest our \$D with an annual return of R% and take annual withdrawals from this investment portfolio so as to last until we're half-way to 90 years old ... and, if we're now at age A, that means we withdraw for Y = (90 - A)/2 years.

There's a neat formula for this and it's:

 \$P = \$D R/(1 - (1+R)-Y)

An Excel spreadsheet will have such a function: PMT(R,45-A/2,-D)

>Why "half-way to 90"?
Some people drop dead early and their money helps pay the annuities for those that live longer than expected so that ...

>But why "half-way to 90"?
Because ... uh, it gives an estimate that's ... uh ... not bad.

>Why not "half-way to 92"?
Sure, we can try that. In fact we can vary that interest rate R as well and get some pictures, like so ...

Remember, we're talking ballpark here. However, if you get a few quotes (appropriate for your particular situation) I think you'll be able to find an internal rate which generates a reasonable estimate of the quotes (and that internal rate will most probably be in the range 0.02 to 0.04, or 2% to 4%) and if the long term bond rate doesn't change dramatically over the next few years, you'll be able to use that rate to estimate the payments if you buy the annuity next year ... or the year after that.). In my case, I bought an annuity (in 1993, at age 59, guaranteed for fifteen years, my wife receiving the full payment when I drop dead) which had rate = .04 (or 4%). The annual payment was 9.1% of the purchase price of the life annuity ... and I used the magic formula above for a number of years to determine if I should buy more ...
... but I found that buying and selling stocks was so much fun that I never got around to buying more. BUT, when I'm seventy ... maybe.

P.S. You may want to take a peek at this chart.

another P.S. re the (approximate) formula above ... this is a fixed income ... no protection against inflation!

a final P.S. Here, you can play with the formula above.
(We'll use half-way to 95 but you can try different Rates, like 2% or 2.5% etc.
 Amount =\$      Your Age =       some internal Rate (example 2.5) =% Approximate Annual Annuity =\$