Hi, I have a query in Q 2.8, in chapter 2, on page 22. Can anyone explain me me the derivation that follows the expression? Thanks for your help! Regards, Shyam
Expression \( V^{n} \require{enclose}\ddot{a}_{\enclose{actuarial}{max\left(K_{x}+1-n,0\right)}}\) is annuity deferred for n years. The present value is maximum of for duration Kx+1-n or 0. If life survives for n years then \(K_{x} + 1 - n\) and if dies before n then 0. Here you can think whole life annuity minus temporary annuity for n years. Now coming to derivation. 4th line - the term inside bracket \(V^{max \left(K_{x} + 1 - n + n, 0 + n\right)} / V^{n} \) the rest follows simple math. Now present value random variable given on next page. it is assurance same like guaranteed annuity for n years. So if life dies before n years or after n years there is benefit.