In chapters 3 and 5 we looked at payment streams - continuous payments and force of interest - continuously paid interest. I believe I get the concepts separately but can't see how they work together. As I understand it "a bar n" and "s bar n" are constant payment streams with constant forces of interest - is that right?
Sounds right. It might help to think about a time interval between t and t+dt. At t, you have an amount; at t+dt you have that amount, plus continuously compunded interest, plus the continuous payment received during the interval.