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Greetings, Leo, and welcome. You asked:

I am vested in a local gov't retirement plan. I have not worked for the city for about 13 years. When I turned 50 - three years ago - I was eligable to start receiving payments. I have not yet elected to do so. As in other plans, the later I start receiving payments the higher they will be. Once I start the amt is essentially fixed, except for a cola.

There is no easy or pat answer to this question. You are correct that essentially you could do a present value analysis of the two income streams based on your life expectancy. In your case, the annuity provides a COLA increase, so just assume a rate of return equal to the inflation rate you choose. I don't know where you could find an online calculator to solve for the present value of an annuity due, but any financial calculator will work.

N = your life expectancy at the time the annuity starts
Pymt = annuity amount
Return = assumed inflation rate
Future Value = 0

Solve for the present value of an annuity due.

One set of computations will be for the annuity starting today, and the other for the one starting at normal retirement age. When you find the present value of the latter at normal retirement age, do a second computation where the solution becomes the future value, N becomes number of years from today to normal retirement, and return is your assumed inflation rate. Solve for present value. That answer becomes the one you compare to the present value of taking the annuity starting today.

Those gyrations are pretty much the easy part. The hard part is deciding on how long you will live, what assumed COLA you should use for inflation, and what you will do with the annuity if you receive it now. If it gets saved instead of spent, then the calculation has to take that into account as well by seeing how much those savings will increase any payment you would get starting at normal retirement age. Or do you intend to retire early anyway? :-) The list goes on and on.

Regards..Pixy