I don’t think many people explain it this way, but it is probably the best analogy I’ve heard. Rent is paying for the “use” of something: like renting a movie, an apartment or house or a car. You never own the item, but you get to enjoy the use of it for a specified period of time. Interest in the financial world is exactly the same thing, except you are renting money!
If you go back to the post that talks about how banks make money on your savings account, you’ll remember that they give you interest, but take your money and give it out in the form of a mortgage at a higher rate of interest. So they are “renting” the use of your money and paying you “rent” in the form of interest. They are also turning that around and renting it out to the mortgagor who pays interest on their mortgage (rent TO the bank).
To take the example even further, if you were a landlord and renting out a room, the rent you collect is taxable as income. It’s just like earning money from a 9-5 job. Similarly, the interest you collect on your investments is fully taxable as well (not to be confused with “Dividends”, “Capital Gains” or “Return of Capital” distributions). Even the interest you collect on your savings accounts is technically taxable income. The banks will send you a form (a T5) that indicates the amount of interest you earned and have to report on your tax return. However, they generally don’t do this if the interest amount is less than $50. But if you had $100,000 in your savings account they certainly would send it out, and you certainly would be expected to claim it and pay tax on it!