The win-win situation, I meant to imply that both the financial institution on one hand and the client on the other are satisfied with such interest rate (r) for a given portfolio.
There are two versions of the answers. First, a bunch of guys, primarily bankers or bank owners, meet every morning over coffee, then decide how much they are going to charge each other (interest rate) on interbank lending.
Second, interest rates are determined by the growth experienced by any economy and, not the other way around as lectured in mainstream economics textbooks. This has been proven empirically just recently by Prof Richard Werner. You may want to listen to this https://www.youtube.com/watch?time_continue=2&v=txc8yuEeG_c&feature=emb_title
Or read this Reconsidering Monetary Policy: An Empirical Examination of the Relationship Between Interest Rates and Nominal GDP Growth in the U.S., U.K., Germany and Japan - ScienceDirect. Article Reconsidering monetary policy: an empirical examination of t...
I have experienced this situation many years ago while I was in banking industry in late 1980s and early 1990s. Inflation and interest rates were very high back then, over 100% a year. We as a bank would enter weekly Central Bank`s bidding of treasury/government bonds and buy a portion of it and sell it to customers at 2% lower than what we would otherwise get from the government. It is a win win situation. We as a bank gain a commission, customer gains a return over and above the inflation.
The common sense approach towards answering this question is to consider Financial Institutions as only "part of a subsystem of a System" (notice the capital letter!). The System is that which in simplest terms must be considered as being the general economic system and structure of a nation. Certainly the rates which financial institutions apply for their services (on both sides of their balance sheets) is a reflection of the supply and demand of their services from other sectors of the economy.
But these other sectors too are engaged in debtor-creditor relationships and hence a cost-of-money relationships approach is effective between them and also with the other sector of i.e. financial services. So industry, retalining, agriculture, the financial sector, and even government itself, are all part of a single coherent relationships system (indeed a market!) that has as its core underpinning the application of a price, i.e. the rate of interest.
Within then of course the sub-system, that is the financial services sector on its own, there is always in place the core price system. When banks engage in inter-bank lending, be it on a day-to-day basis or on a timespan basis, they are participating in that specific market and one sees this, again, in its various component sectors. To name only a few: the FOREX (foreign exchange) market (including part of this, the forward exchange market), the spot deposit/loan markets, the market existing between central banks, etc, etc.
All of these are factors which effect the "r" of interest rates.