This is my attemp to set the half-life of US dollar inspired by this chart on pricedingold.com.
Assume that you had stuck $100 bill into your mattress at the end of the year 1969. Nominal value of bill can’t change, it looks like this:
But government has created much more money since then and the real value of your bill had declined. After adjustment for M2 money-supply the story looks completely different. Out of initial value, remaining value and time of decay is possible to calculate half-life of this bill (i.e. savings). Result is 10.47 years. The US dollar is losing half of its value every 10.5 years. Notice the smooth curve without major fluctuations. Money-supply can provide much stable benchmark than price of gold I think. This chart shows value of $100 bill adjusted for inflation (M2 adjusted):
But because of diminishing household income, the value of this bill can be a little bit higher. Because it is harder to make money nowadays. The half-life of US dollar after adjustment for M2 & income is 15.76 years.
Conclusion: Half-life of US dollar is probably not 4 years as pricedingold.com states. Prices are not doubling every 4 years or so. 16 years seems to be more realistic estimate. Anyway the only important question is for how long will public’s trust in paper money last. America had abandoned gold-standard in the year 1971. Since than there is officially no brake for money printing. Negative interest rates on money in Europe and Japan (absurdity never seen in history) shows, that we are (after only 45 years) approaching the end of paper money.