In free market economies, banks set deposit and lending rates based on competitive market forces (e.g. balance sheet considerations, capital considerations, competition, cost of capital from other sources, etc.). How did this work behind the Iron Curtain?
I can comment on Czechoslovakia prior 1989, which had centralized planned economy where the decision was made from the Central Planning Committee and Ministry of Finance. The Czechoslovak banking system had four banks, from one served as a Czechoslovak State Saving (divided in 1968 into Czech and Slovak branches) house where people deposited their money. Other three served for the needs of the state with foreign companies or for people who worked abroad as the Czechoslovak currency was not convertible. The saving and banking deposits in the country were regulated by a law of 1964 which defined three basic saving deposits for the people: winning saving account, travel saving account, and regular saving account earning 2% interest. The winning saving account was something like a lottery where a certain number of accounts were able to win 250% in a chance of 1:1000, 100% in a chance of 3:1000, and 20% in a chance 21:1000 Saving lottery law regulation.
The regular saving accounts were either term or no term. The term accounts were set in 1970 as 3% interest rate for six months or 4% for a year or more. In the 70s, the country started with non-cash payment by transferring funds between accounts, usually for large purchases as consumer loans for cars, appliances, electronics, and furniture became popular. The interest rate on the loans were low and set by the government. In the later years of the communist regime, younger people were encouraged to put money into savings, encouraged to do so for about 5 years where they would get the 2% interest plus bonus, which would be around 3%, so these accounts would earn over 5%.
The money within the banks were channeled back to the state, but since the amount of goods was limited, the saving rate (around 3% in the 80s) was higher than overall consumer debt. In the late 80s when the economic problems could not be hidden, the lack of liquidity between state own companies and state businesses caused that many of them stopped paying their suppliers or were not receiving money for their products. The country was pretty much insolvent in the 1988.