Great discussion here. Let's do some math. Assuming $3.60/lb as the current copper price, and assuming $2.35/lb as the current wholesale copper price (I got this from the current wholesale scrap price of roofing copper, which is roughly equivilent to a cent, I believe), you should get a wholesale selling price of 65% of full market value, on average. There are 145 copper cents in a pound, which would give you a current profit of 62% over face value. So, each cent is worth $.0162 scrap value currently, at wholesale.
Assuming $10/lb as the price in 2033, and assuming $6.50/lb wholesale price (going by the 65% discussed above), you would make 448% over face value, or a value of $.0448 per cent. Amortized over 20 years of holding onto it, you are making approx a 7.75% annual return on your investment. As a comparison, over 20 years, you would make between 1-4% in a money market acct (depends on interest rates), 3.5-8% on bonds (again, depending on interest rates), 8-9% in the S&P 500 in the stock market, or 9-10% in the stock market with a risky portfolio that was well diversified.
Copper prices are speculative, meaning that it could be $10/lb in 20 years or $2/lb in 20 years, who knows. Investing in money markets and bonds give you a guaranteed and insured rate of return, while stocks give you a riskier rate of return, but over a 20-year period, stocks have always made money, unless you owned stock before the 1929 stock market crash, then it took you 24 years to make money again.
In addition, bullion metal investments, of which penny hoarding is, are taxed at a maximum 28%, depending on your income level, whereas capital gains, of which the other investments I mentioned, are taxed at only 15%, if you earn less than $250,000 per family. To make it worth your while, copper would have to go up to at least $12/lb, and the current law would have to be changed, for someone to just break even over a more mainstream investment strategy. Also, copper (and all metals) are at historically high prices right now, which makes the odds of them going even higher, much lower over time.
You make the call, but these numbers tell me that investing in large hoards of copper cents will not pay off compared to other investment types, even if the price goes up to $10/lb in 20 years. I could be off on some of these numbers as well, but this is just an example.