In the final paragraph of chapter, core reading says that force of interest is the most fundamental measure of interest (as all other interest rates can be derived from it) . But can't all other rates be derived from other rates too? Like if we take effective interest rate for ex., i understand that, from effective interest rate, one can find equivalent rates of all other kinds using various formulae in the chapter.
Yeah I see your point but I think you’re missing the case where the rate changes over time. If you fully specify a formula for the force of interest over time, this gives unique solutions for what the other rates can be. i.e. you can derive all the other rates from it. However, if you specify an annual rate (for example) which applies over a year there are many different possible changing forces of interest which could have produced this annual rate. It’s only if you assume that the force of interest must be constant over the year that there is a unique solution. I assume this is what it means when it says the force of interest is the most fundamental measure of interest. Of course if you want to be pedantic you could say: “well I can just specify a function defining an annual rate of interest for all times t - this is just as fundamental as a force of interest because all other rates over any period would be uniquely defined”. I wouldn’t argue with this, I’d just say it’s less than natural to specify an instantaneously applicable rate of interest at time t in terms of what its annual equivalent rate would be and call that the fundamental quantity. Since if it was changing continuously through time, it could be an annual rate of 16% one instant, then an instant later be 15%, then an instant later be 20% - none of which might ever be applicable over even an entire second let alone a year. Hence it makes sense to think of it as a force of interest instead.
