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Combine age contract

hey guys it's MJ the student actory and we're going to be talking about chapter one for subject CT v which is Life Assurance contracts now basically you just need to know this diagram to understand the theory behind this chapter essentially Life Assurance contracts are based on life and in life two things can happen you can either survive in which case you get a pure endowment or you can die in which case the whole life assurance kicks it so what I mean by the pink one being pure endowment based on survival means that if you survive to a certain age this contract will pay you money if you die this contract will pay you mate now this contract depends goes infinitely into the future so if you put an expiry date on it it becomes known as a term assurance and if you combine the term assurance and a pure endowment you get something known as an endowment assurance these are the four main life assurance contracts and yeah now I'm going to go and talk a little bit about the mathematics behind each one just remember to understand the mathematics behind this video you will need to understand the probabilities that are explained in subject ct4 but just a quick recap tqx is the probability that a life aged ex dies within two years and Joe you just sum up all the times that it's a lot and then when it dies immediately feel free to pause the video and read all my little side notes and then TPX is the probability that someone who's aged X will survive T years and remember that formula from CT for it's just the negative of the total force of dying which gives you the chance or the force of staying alive okay but yup let's see T for stuff CT v stuff starts with this whole office Durin's this is the most simplistic contract what it basically does is you take it out on a life and whenever that life dies you get paid a sum assured so the payment is made on death so the present value would just be the discount value of the expected life of the person plus one because it's this is the simple case with discrete where payments are made at the end of year of death the symbol for the expected value of this value here is known as a X and it is simply the summation of all the instances where the person survives a little period then dies Plus that they survive a little period and dies plus a little period and it dies and that the survival is represented by kpx and the death is then Q X plus K for the age feel free to pause and read my little notes in the white variants you'll see that this formula is going to be the same with all the terms and it's also I mean this...