When will gold's (NYSEARCA:GLD) price recover? This question has to be on the minds of even those investing in gold solely for the long term. With all of this noise in the background on why gold's price is behaving the way it is, I decided to come up with a mathematical model to predict the price of gold based on its own history and the expected future inflation rate. By the end of this article, you too will be able to calculate an estimate of gold's future price just based on a couple of straightforward factors.

Gold has had a remarkable run in the last two decades as the chart below shows, both in terms of absolute price appreciation and inflation adjusted price appreciation. Based on this historical data, we can use expectation about future inflation to calculate a range of returns for gold over the next few years as I will discuss in a minute.

Since the start of 2012, gold has declined significantly in price, as have most major gold miners including Barrick (NYSE:ABX), Newmont (NYSE:NEM), Goldcorp (NYSE:GG), Yamana (NYSE:AUY), and Kinross (NYSE:KGC). This effect is in part driven by increased supply of gold as shown in the chart below, and by decreased demand from institutional investors and some governments, but it may also be partially driven by increased interest in a new currency - Bitcoins.

Adding to gold's demand declines, I suspect that the increased popularity of Bitcoins is leading some individuals who were interested in investing in gold for the short term to invest in Bitcoins instead. A recent Businessweek article supports the thesis that Bitcoins are becoming more mainstream and popular.

One important question for investors in gold, however, is will the increased volatility of Bitcoins drive these investors back to the stability and long term history of gold?

If Bitcoins continue to fluctuate wildly in value as they have in the recent past, then many individual investors are likely to be dissuaded from investing due to the risk and volatility. The US government's crack-down on the nascent currency recently only adds to these risks. If the Bitcoin can survive and become more widely accepted as a payment medium however, then even more investors in gold may flee to the new online currency, since it shares many of gold's attractive monetary properties, but is much easier to store.

The chart below uses the real price ratio between gold's spot price and the US CPI on the right side axis, and the level of future inflation on average over the next ten years in the horizontal axis. Note that in red I have highlighted the historical average real price ratio; 3.2. I have also highlighted the 2% column for inflation based on past inflation levels. Using the intersection of these two figures gives you the annualized real rate of return for gold (-6.03% annually in this case). If on the other hand, we experience average inflation of 5%, and gold stays at the current ~7.2 real price ratio (see chart above), then gold will have an annual return of roughly 4.90%. (Mathematical note: The calculation is based on the current CPI and the inflation factor chose as follows. Price of Gold in Ten Years = Real Price Ratio * (CPI * (1+Inflation Rate)^10) The annual return can then be backed out based on the current price of gold and the projected future price. Since the price of gold changes all the time, the specific figures in this table will change slightly as well.)

So in summary, given the recovering economy, and the newfound skepticism by many institutions towards gold, those investors not willing to hold on for the long run should exit the metal. Long term gold investors who do choose to hang on need to hope that as the reign of fiat money continues, inflation will eventually return to its historic 3.7% rate, and that gold prices will eventually recover. Uncertainty in Bitcoins could drive people back into gold, but if Bitcoins overcome their present difficulties, the new currency could also become an even bigger competitor to gold.

Assuming inflation falls in the range of 2-4% over the next 10 years, and gold returns to its historic real price ratio of 3.2, gold will be at $984 per oz. in ten years' time. If however gold stays at the more recent real price ratio of 7 or so, then gold will trade at $2,154 in 10 years time (again assuming inflation of 2-4%). Thus gold investors need to decide if gold's lofty price levels in recent years are a bubble, in which case, the future of gold is not so bright, or if they represent a change driven by increased central bank intervention, in which case, gold has a promising outlook.

**Disclosure: **I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.