Unexpectedly Intriguing!
March 28, 2005

Since looking at the Reid/Schumer Social Security calculator, I've had a nagging question about how the Democratic Duo went about determining the size of the payment you would receive from a Personal Retirement Account (PRA) under their math. The only guidance provided by the Democratic senators is in this 1-page PDF document, which says:

... the calculator converts your individual account into equal annual payments (e.g., if you have \$100,000 in your private account, that can buy an inflation-adjusted annual benefit of about \$7,000).

And that's all it says regarding how the money you would have accumulated in your account over your working life will be paid out to you in retirement. Obviously, they're talking about an ordinary annuity, but this leads to two basic questions:

1. What kind of inflation-adjusted rate of return are you getting from the annuity?
2. How long will the annuity provide payments?

Of course, when we have questions like these here at Political Calculations(TM), we like to throw a nice, simple calculator together to do the math. The problem is that in this case, the calculator that would directly solve for the annuity's rate of return or for the term of the annuity really wouldn't have much utility in the aftermarket for the tools that get developed here, since people who would pursue annuities as an investment vehicle would already know these things. So, instead of doing the math directly, I'm opting to do the math indirectly by providing a tool that determines what the regular payment for an annuity should be, then playing with the numbers until I get answers that match the Senators' assumptions. That said, here's the tool:

Investment Information
Input Data Values
Starting Balance (\$USD)
Rate of Return (%)
Term of Annuity (years)

Annuity Payment
Calculated Results Values
Annual Payment (\$USD)

The rate of return default value of 4.25% provided above is taken from the government's Thrift Savings Program's Historical Annuity Rate Index for April, 2005. This rate of return is not adjusted for inflation - the easiest way to do this would be to subtract the inflation rate from the rate of return. The long-term rate of inflation in the U.S. is 3.3%, which means the inflation adjusted rate would be roughly 1.0%.

I have also arbitrarily set the default value for the term of the annuity at 20 years. This figure matches up with the upper end of average life expectancy for someone who retires at age 65, at least according to Social Security. In reality, if you plan to rely on an annuity for retirement income, the term should be paced by your remaining life expectancy once you retire, which is in itself a topic for another day.

For this project however, I kept adjusting the rate of return until I produced numbers close to those published by the Democratic Senators (\$100,000 starting balance producing \$7000 in annual payments.) I calculated the following numbers for the indicated investment term:

Calculated Results
Term of Investment (Years) Inflation-Adjusted Rate of Return (%)
10 -6.009
20 3.443
30 5.657
40 6.420

It's left as an exercise for the reader to determine how realistic these values may be.

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