 Hey guys, this is MJ, the student's act tree, and this is CT5, Chapter 13, profit testing and reserves. I like this chapter because it's actually very easy, it's very simple, and it's almost like getting free marks. So without further ado, let's jump straight into what it is. Essentially, what we're going to do is we're going to be talking about this whole thing known as zeroization. It's a strange word to say, it's zeroization technique. And basically what it is, it's a method used for creating reserves, hence why it's called profit testing and reserves. So let's get to it. To calculate the last non-zero reserve, so I mean there's all these formulas that I could talk you guys through, but what I did was I created my very own diagram, so instead of having to read through all of this, like the textbook gives you, I decided to draw a very nice diagram. And here it is, it can't all fit in the screen at once, so we'll start here. What you do with zeroizing is you'll have your profit vector. Let me see if I have an example of a profit vector. Here's an example of a profit vector. Sorry, I'm jumping up all around but you'll see why. So we've got this profit vector here and what we want to do is we want to zeroize it. I'm not even going to try that. And how are we going to do that? So that's what we have and this is what we want to result in. So what you can see with this profit vector is that the only negative value that should be appearing is the first one. All these others must either be zeros or positive values. So you can see over here we had a negative value here and a negative value here. So what we do is, so bearing that in mind, let's look at my diagram. And first step are are there any negative cash flows after the first year? And the answer is yes. That was number four. Number four is negative. So yes. So start from the last negative entry and calculate the reserve one year before. And that's where this formula here comes in. So it's the reserve one year before is going to be equal to the cash flow. Make it negative divided by the interest. So we set up this reserve. So for here, negative 10.82, we set up this reserve at time three. Three V is equal to that, that divided, you can see it's a little bit smaller because of the interest. So now what do we do? We go back to our little diagram. It says this zeroizes the entry and decreases the one before it. So what we do is we now use the purple formula. And what this is saying is the non-unit cash flow of the year before now needs to decrease by this reserve that we've set up. Times it by the probability that the person survives to that age. So if we come to our example, this is now for year three. We take its existing value and we subtract it by the reserves. Times the probability that the person is still alive and we get 79.09. Which if you see at the end is what we got over there, 079.09. So let's go back to our diagram. Is the entry before positive or negative? Is the entry before it positive or negative? And in our case, it is negative. So what we need to do is, oh no, no, sorry, this entry is positive. It's positive because 89 becomes 79. So we say positive and we come back here. Any negative cash flow after the first year? And the answer again is yes, because the second cash flow is negative. So now what we do are the exact same steps. We're going to do the blue. We're going to do the purple and then we're going to check again with the white. So those are our formulas in our example. Year three is positive, so you can see we went good, but year two is negative. So we set up another reserve at year one, which is 5.02. And we then zeroize and decrease the non-unit cash flow at time two. And at cash and at year one, we get negative 45.90. Which is fine because that's the very, so any negative cash flows after the first year, the answer is no, so we are finally done. And job. So that is actually how simple this whole thing is. I don't know if I complicated it, but I get this, it makes perfect sense to me. What you're doing is you're making it zero, you're taking that value, you're putting a chair, you're just decreasing it by interest and force of mortality, you're checking if that's positive and then you just keep repeating the thing. I made a little cheat sheet. So let me just push it up here a bit. Here's my little cheat sheet. You can see I use a different app that's what's on the white background. And this is basically, if you didn't understand anything I said, learn this off by heart and you should actually be finding the example. I mean, this is an easy question. You should be getting these marks. But job. That is chapter 13. It's the penultimate chapter of CT5. So I hope you enjoyed this video. Please hit like and subscribe and leave me a comment in the comment section below. Thanks guys. Cheers.