Printed document lifespan
I will interpret the question as you wanting to know how long it takes until a black ink inkjet print noticeably fades.
As with many artworks involving colourants, keeping prints flat in a dark, cool, (atmospherically) stable and pure, and dry place will preserve them for the longest period of time.
Make sure the envelope you're using is made of acid-free paper, as acid can break down the chemical compounds of both the paper.
Similarly, use gloves when handling the print to avoid transferring acids and other contaminants to the print.
Relative humidity should be kept stable somewhere between 30 - 40%, the temperature around around 0° Celsius (32° Fahrenheit) ideally, or between 18 en 21° Celsius (65 to 70° Fahrenheit) when stored in your house, and the air free of pollution (&quot;sulfur dioxide, nitrogen dioxide, ozone, peroxides, and formaldehyde&quot;). source
Kept like this, based on this article and the values in the adjacent table, your print could remain visually unchanged for over a century:

click image for larger version | source

Of course, as for the larger question here, apart from the environmental conditions, the longevity of prints is determined by a range of options that need to be selected carefully for the intended purpose.
I assume you know this already, as you mention the type of paper, but both the ink and the paper used are important for print permanence.

The inkjet ink will be either pigment- or dye-based.
Pigment-based inks last longer, since they consist of much larger particles: they are more stable, retain their colours better, and are less sensitive to environmental factors.
For a more detailed comparison see this related answer.

The paper used is important for the bond that the inkjet ink will form.
The paper should be acid-free, too. Coated paper specially intended for inkjet printer prints lets the ink bond better, resulting in improved ink stability.
Inkjet paper, fine arts paper, permanent paper, archival paper (wood pulp/cotton rag), swellable polymer coated papers (for dye-based inks, a coating that encapsulates the ink), and microporous coated papers (for pigment-based inks) have an increasingly longer 'ink-life'.
You can read a more detailed study of the preservation of prints, diving deeper into these particular factors, on this page of the NEDCC.


Even though, depending on your printer and settings, the black ink might be composed of a variety of colours, &quot;'black and white' prints are vastly more stable&quot; source.
Also, note that different brands, manufacturers, and models of printers have different technologies, inks, and qualities. And your printer settings will have an influence, too, if only for the amount of ink used for the print - even the font you use has consequences for the permanence of the print, as this study (pdf file) shows.
The conclusion to be drawn is that it's hard to tell how long the print will last, as there are too many factors involved.
A great general resource on print permanence is the Wilhelm Imaging Research website, full of studies and tests performed to find out the longevity of printed materials.