Reserves
I refer to 2008 material...and I guess you are referring to the section calculating net premium reserves for endowment assurances... (it is on p-24 in my material). if this is not the one you referred to, please let me know...
You can expand the second term. That gives you two terms a x+t:n-t/a x:n
(dots on 'a' continues..i could not put them here..), and another term (d x a x+t:n-t). This last term is same as second term, but only when bases for reserve and premium calculations are same. For example, if interest basis is different in reserve and premium calculations, then value of 'd' differs and so those two terms would not be same. So, you need that assumption of same bases to cancel two terms leaving the other two terms in final result.
please discuss if i was not clear...it is a bit hard to explain without putting notations...!!!! I did scan a manuscript, but size limitations of the forum does not allow me to attach it !!
Thanks,
Raj