Obviously, just about any savings account will let you enjoy compound interest, but as you realize rates of 0.05% will never yield (heh!) any appreciable growth of the balance in your lifetime.
However, here is an arrangement that would allow you to enjoy the benefit of compound interest at a reasonable rate of interest with relatively low, manageable risk. (I should note that it is possible that this type of negative amortization loan is not legal, but I would think that if reverse mortgages are allowable, this would be as well. It is not something I have actually looked into; it is just something I came up with in an attempt to satisfy your desire for compound interest at a reasonable rate with low risk.)
Yeah, just to be sure, I am not seriously recommending that you try to do this. This suggestion is just for your entertainment only:
Find a person who owns their house or other real estate free and clear, but is strapped for cash. The age range you should target will depend on how long you want to allow your money to compound. If you want it to compound for a long time (30 years or so), you should look for someone 45 to 55 y.o. or so. If you will be happy compounding interest for just five years or so, look for someone much older.
Offer him/her a mortgage on their property with the following terms. You will loan them $10,000 against their real estate, at an interest rate of 7%, or whatever you can get. They will never need to make a payment on the loan while they are alive. Instead, the interest will accrue to the balance of the loan. As the balance builds, the interest compounds.
When they pass away, the loan becomes due. The heirs may need to sell the property to pay off the loan. But when they do, voila! You will enjoy the miracle of compound interest that you crave! For example, if you are able to loan $10,000 at 7%, it will be worth over $76,000 if your borrowers live 30 years. At 5%, it will be a not too shabby $43,000.
Now, this is not something for a novice to do, and I am not seriously recommending that you try to do this.
Potential pitfalls off the top of my head: You would need to assess the property to be confident that its will retain enough value so that proceeds from its future sale at some unknown date will be able to cover your loan. (It is therefore essential that the initial loan be only a small fraction of the value of the property.) You would need to ensure that real estate taxes are paid every year, and that the loan gets paid off if the owner chooses to sell the property before they die. You would need to ensure that they maintain adequate insurance on their property.
There are risks as well, but not so many that are different from risks you would face in a more conventional compound interest savings vehicle.
There is the risk of rampant inflation destroying the value of your money. There is the risk of war or some other event that would not be covered by insurance destroying the property or the value of the property. There is the risk that the party you loaned the money to outlives you, but at least your heirs would eventually get paid. There is the risk that the property ends up being worth less than the amount due on the loan in the future. There is the risk that despite your best efforts, you somehow get defrauded and lose your money.
And of course you will face legal fees in setting up the loan, etc.
Plus there is the whole bad kharma thing of waiting for someone to die so that you can get your money.
And I am sure there are numerous other potential risks and pitfalls that I have failed to list here.
Your other alternative is to wait. Interest rates will go up again someday, and then you can set up a typical saving account paying more interest. Of course, inflation will likely be higher as well.