This post covers the same ground as my previous post, but it's written for a different audience. It's written for those people who approach monetary policy from a banking/finance perspective.
Suppose you are running a commercial bank. Let's call it "BMO". And let's simplify massively. On the asset side of your balance sheet you have "loans". On the liability side of your balance sheet you have demand deposits. Let's call those demand deposits "BMO dollars", because that's what they are.
Again simplifying massively, you have three instruments, or control levers:
1. You set the interest rate on loans. Yes, you have to watch the competition when you set it, but you set it. (And you also care about risk, term to maturity, liquidity, etc., but let's abstract from those things.)
2. You set the interest rate on deposits. Yes, you have to watch the competition when you set it, and you might set it at 0%, or even negative, but you set it. (And you also set fees for cheques, and paying bills, etc., but let's abstract from those things.)
3. You set the exchange rate at which you promise to convert BMO dollars into Bank of Canada dollars. And you fix that exchange rate permanently at one, of course.