Core reading, pp. 742. Proof of equality of reserves, whole life assurance example. The proof makes sense to me, other than that where the IFoA say 'Rearranging the terms, we will obtain the expression for the retrospective reserve'. It is not obvious to me how these terms are rearranged to get the expression for the retrospective reserve. Could you explain the relationship between the 'modified equation' and the retrospective reserve equation, and why/how the terms can be rearranged to yield this?
It's similar to the alternative way of approaching it, which is presented on page 28 of Chapter 20 of ActEd's course notes. But if you group the terms with the same multipliers together, eg the two terms with S together, and then simplify you'll end up with the terms in the retrospective formula.
