## Annuities

So looking at an explanation of ordinary annuities, it says that for a payment of $R$ after $n$ payment periods, with interest rate $i$, is described by the table:

Payment...............Conversion Periods.............Amount
1.........................n-1.................................R(1+i)^(n-1)
2.........................n-2.................................R(1+i)^(n-2)

... And so on. What I find a little odd about this is that, at the last payment period, no interest is charged. It seems like the basic way this works is: Get a loan or whatever, and at the end of the first payment period, you pay back a portion of the total, and then pay interest on what's left. But the business which loaned you money seems like they're losing an opportunity to charge you interest on the money you've been using up until the end of the first payment period. Am I misunderstanding something, or is this just not something that businesses care about?