Banks keep trying to get people to go paperless. But they are quite ungenerous with their terms -- generally offering to keep the information available on-line for only a year or two.
I don't understand that. I would gladly go paperless with the bank if they would offer something more reasonable. Frankly, I don't think 31 years is unreasonable -- the statements are tiny. It would be VERY rare you'd need something that far back, but I'm picking 31 years just because there are lots of 30 year mortgages. At 31 years you'd be very safe, especially if they sent yearly statements with your 1099 form and you tucked those away.
If we assume, for a moment, a file size of 5k per customer per year [insert any number you want; don't make it too high because there's no formatting or anything]
On my desk, purchased from Iomega for less than $100, is a 500 gig hard drive. That would accommodate approximately 100,000,000 customer-years of statements. Assume you are storing these twice [so there's backup], and add another $100.
Sure, you'd probably need some hardware and a simple interface for retrieval -- but not that much. Retrieval is going to be by indexes [soc security number --> pick an account, and month] so it wouldn't hard to find the right records.
Now every customer-year of statements has to cost at least 50 cents * 12 = $6 to mail out (postage and printing; I think I'm probably low). So, that 100,000,000 customer years would represent $600,000,000 worth of postage saved at current rates.
So, even if I am off by several orders of magnitude, the bank should offer basically time-unlimited statement storage and retrieval as an incentive to save postage.
So why don't they?
One theory might be merger and acquisition activity. There's a lot of this. The bank I started using in the 1980's is still in the same physical location, but has its 6th corporate owner [Glenview Guaranty, 1st Wilmette, 1st Chicago, NBD/1st Chicago, Bank One, Chase].
But that's easily solvable by the banking industry coming up with a set of electronic data interchange standards for this situation. Note there is already substantial electronic data interchange in financial services in a standardized format [e.g. electronic bill pay].