Can you elaborate on this a bit? In my understanding, interest is a return on productive business, and money can only return interest if invested in a productive business. It can't return interest just by itself, and banks/owners of money won't loan it to anyone unless they expect that someone to be productive, and thus provide the "money interest" through their own work.

Its perfectly related I think:

All entrepreneurs and businessmen decide, how much capital they need and what price they are willig to pay (maximum their expected returns of investment). When there is a lot of growth in the economy - probably due to a new sector emerging - there is a lot of demand for money in the market. The price (interest) is given by supply and demand. Imagine Google offering 20% interest if you give them your money, this would convince a lot of people to supply their beloved money for some time. So some really profitable entrepreneur is always given money if he can "outbid your timepreference".
Here you can also derive the growth-interest-relation. If there are 9 companies having returns of 5% and one company having a return of 4%, the latter might be outbidden by the others when interest rate climbs towards 5%. As 5% ist reached, there is an equilibrium in the moneymarket and the 9 companies won't borrow more money, unless supply increases (and interest frate drops) or their expected return rises beyond 5%. So growth determines the interest rates (as long as central banks leave their noses out) into an equilibrium where there are only companies beyond that interest rate.