Interaction between productivity growth and interest rates Isabel Schnabel, Member of the Executive Board of the European Central Bank point at the interview out "The real interest rate (...) emerges from the economy’s growth potential in the long run.“ https://www.ecb.europa.eu/press/inter/date/2020/html/ecb.in200211~d2b4afb5d3.en.html

Another article also touches upon this question "It is well-known that productivity is a long-term determinant of return on capital and thereby of interest rates, which explains why there is a positive correlation between these two indicators" https://www.clevelandfed.org/newsroom-and-events/publications/economic-commentary/2017-economic-commentaries/ec-201720-productivity-real-interest-rates-long-run.aspx

However, for me it seems counter-intuitive. If productivity is low i.e. growth is week, than the risk to lend is high, meaning the lenders would demand higher premium for the risk -> IR would be higher on average. Can you please come up with an explanation on why slower productivity growth would result in lower interest rates?
Starting at the end, the simple answer is that intreset rates are decided as a counter measure for slow growth, which may derive from productivity slump. Meaning interest policy is a result, not a cause

On a wider level, the interntion of Central bankers is that there is a productivity rate, internally set in the economy set it's pace of growth. Imagine the added value of internet applications, as opposed to the world before that, as an example.

Their goal, is to set interest rate to match the proper appetite for risk, to encourage that productivity growth: take loans to pay for internet services, as per the example

The main parameter lacking in your equation, is that monitary policy cannot be the main economic policy to encourage productivity. It's the government in general: investinh in education, lowering barries for good healthy markets, provide a supporting legal system for business disputes etc.

Monitary policy can only be effective to a certain extent, in a way, like a wide (regressive) tax deduction