Thanks! I already suspected something like that, because experimenting with values I found out that, if we maintain the same formula, it seems not to be possible to create a curve which still is close enough to our observed price history, but returns significantly lower results for years far in the future. Particularly from 2050 on I get values of more than 10 millions which are in my opinion extremely optimistic.

What I was thus wondering is if you can add an element to the formula to get slightly higher values for the early years, closer to the tops, and slightly lower ones for the more recent years. This would be a formula that is closer to the recent lows of the last 7-8 years, but in the first half would be closer to the highs in 2011 and 2013 for example.

So I continued to experiment, reading superficially some random website about log functions, and found the following formula:

e * 0.8^[ 5,8323 * ln(Date - 03.Jan.2009) - 36.5 ]

Some values I get with this one:

- 2012-01-01: 28.02 € - close to the 2011 high
- 2015-01-01: 651.15 € - close to the 2014 high
- 2020-01-01: 10158.32 € - close to the 2019 high
- 2024-01-01: 41422.95 € - close to the real price in early 2024

Which is quite close to my intentions. Now on to the future:

- 2025-01-01: 55526.39 € - looks quite bearish, but it's possible for 2025 to be an euphoria phase so the real price can be much higher than that.
- 2026-01-01: 73064.35 € - could be close to the low of the next bear.
- 2030-01-01: 190316.34 € - feels already quite good.
- 2035-01-01: 500754.85 € - Gold flippening is close!
- 2040-01-01: 1110794.37 € - Looks already quite bullish, can we sustain that?
- 2050-01-01: 3942264.41 € - I think many would be happy with that result

In contrast the current formula gives for 2050: 19302683.81 € - Looks a bit "unbelievable".

This is only another example for such a formula, and it might be less elegant as it doesn't use the e constant. Perhaps it's too bearish, but I'm more comfortable with it ...