Last week the Bank of Canada cut the overnight rate of interest from 1.00% to 0.75%. The exchange rate dropped 2 cents (about 2.5%) on the news. [Update: I forgot to add (because I figured Canadians already knew it, but then remembered others probably wouldn't) that the Bank of Canada has "done nothing" (with interest rates) for the last 4 years, but the exchange rate has dropped about 20% over the last 2 years. And that's important background for my story.]
Consider a very simple economy with only two goods: apples and bananas. It's a non-monetary economy; apple producers and banana producers swap apples and bananas because people produce only one good but like to consume both goods. So there's a relative price of apples to bananas, Pa/Pb. People borrow and lend apples at a real interest rate Ra (I give you 1 apple today, you promise to give me 1+Ra apples next year); and borrow and lend bananas at a real interest rate Rb (I give you 1 banana today, you promise to give me 1+Rb bananas next year). If people expect (strictly, expect with certainty) that Pa/Pb will stay the same in future, then Ra and Rb will be exactly the same. Because if Ra < Rb, all borrowers would want to borrow in apples, and all lenders would want to lend in bananas, so it couldn't be an equilibrium.