Read some where in Net:= How simple interest can effect whenever time horizon increases.
Note: In the case of a monotonically increasing series, such as the balance of a US dollar bank account with daily compounding interest, every price is above all its predecessors. You can make a claim, then, that no matter how you measure it, the trend is always up.
However, in a larger scope, in a world in which the US dollar fluctuates in value relative to other currencies, and in which banks sometimes fail, a bank account may not actually continue to be a long-term monotonic up-trend investment.
Say we compound one penny at a three percent per year interest rate from year Zero-AD to the present. We get about $5.48 * 10^23, or around a half trillion trillion dollars. Clearly someone in those early days has a penny earning interest, per stories of money lenders in temples. That no such investment survives today indicates severe financial setbacks, from time to time, in which people and whole societies experience collapse and have to start over. Compounding interest seems to work pretty well for a few hundred years at a time.