The question makes use of the formula for a 6th type of reversionary benefit given in section 2.2 of chapter 9. I understand the formula given, and have been able to apply it to answer the question, but it got me thinking whether we are expected to derive in an exam the epv for an ad hoc revisionary benefit using integration. Eg if the formula for this type of reversionary annuity weren't in the notes, would we be expected to be able to derive it in an exam? Or is it safe to learn the formula and the reasoning behind them, and then that should do for questions of this type? Thanks
It's unlikely that an exam question on this material will explicitly ask you to "derive" an expression. It's more likely that you'll be asked to calculate a value (as in the question you mention). In that case, if you know the formula to use, then you should just use it to perform the calculation. If you don't know the formula to use to value the benefits described in a question, then you'll need to work out the relevant formula. A good way to do this (and hence deal with unusual benefits) is to write down an integral expression and try to simplify it - as explained in Section 4.3 of Chapter 9.
In some questions you may find that a combination of reversionary benefits conditions are included, which may appear non-statndard (not listed in the 1 to 6 types reversionary annuity cases in the book work). However, in those cases , you can proceed either by carefully applying integral approach, or by combination of direct formulaes. Its a very good idea to test yourself all the six cases by using integral approaches only. This way , even if some non-statdard case comes up, you can easily maniputae and arrive at the answer.
