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I'm reading the U.S. Department of Labor's PDF Taking the Mystery Out of Retirement Planning. Page 17, Worksheet D, asks the reader to take their total estimated savings in different retirement categories and assign each one an "income conversion factor" based on the approximate interest rate that was chosen. Below is a sample screenshot:

Worksheet D, Monthly Income over a 30-year retirement. Income conversion factors for assumed rates of interest are: 0.004216 for 3%, 0.005368 for 5%, and 0.006653 for 7%. Three columns are provided for accumulated assets, income conversion factor, and monthly income beginning at retirement

I'd like to understand where these numbers come from so I can plug them in a spreadsheet, but no explanation is provided. Is there a formula that can be used to derive these conversion factors?

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It's basically a 30 year annuity calculation. Find an annuity calculator, enter in $1 principal, 30 year duration, and the desired interest rate, choose monthly withdrawals, and you should get something very close to what's in the worksheet.

In reality, the calculator you use may not go to the precision the worksheet does, so you can instead put in a principal of e.g. $1,000,000 and then divide the result by the same amount.

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