All price spreads are rates of interest.
If I buy a good at 10 dollars, and sell it for 11 dollars, the spread between buying and selling prices is 1 dollar. The rate of return is 1/10 or 10%.
Due to this basic truism, we can surmise that the rate of interest derives from individual preferences of time.
Time Preference denotes the value of something ordinally allocated on one's subjective value scale. High time preference, higher. Low time preference, lower.
If a human actor has a low preference of time, they allocate more money to savings. An individual will withhold consumption at a high rate.
If a human actor withholds consumption at a low rate, one will allocate less money to savings and more to consumption.
Austrians understand that high savings=low rate of interest, and low savings=high rate of interest.
In basic economics we are given the theoretical formula of savings=investment.
Austrians can suggest that due to value being subjective, savings and investment might not be equal. This difference is decided by time preference. The mainstream may call this hoarding.
Taking the idea of price spreads from above, we can demonstrate that the rate of interest is the rate of return, which ultimately are the price spreads.
The individual human actor wields the subjective fortitude to profess his investment-consumption ratios similar in respects to the theory aforementioned.
If his income is 100 dollars, he may decide to consume 10 of that 100. In a similar fashion as the above example, the resulting ratio would be 1/9, 10 dollars would be allocated to consumption, and 90 dollars would be withheld from consumption which is allocated to savings.
The ratio delineated is a rate of return, which is 11%. Continuing the basic rubric, one can see that this would be a rate of interest.
Conclusively we arrive at where interest rates begin, or where they evolve from. The rate of interest is a subjective value that derives from individual human action.