In this workout, we've been told that an insurance company has written a book of insurance policies on the last day of year one, and we've been asked to calculate the claims reserve at each balance sheet date and the claims expense for each year throughout years one to three.

Now, we're assuming that the actual claims are as expected, and 80% of claims are paid in the year after they're incurred.

Now, the premium written is 100, and that's all written and received in year one. So there's no premium written in years two and three.

Now, the coverage period for the policies is two years, so effectively, the policies are in place throughout years two and three.

And finally, the loss ratio is 84%, which means that out of the premium written of 100, the insurance company expects to pay out 84 in claims.

Now let's calculate the net earned premiums for the policy.

And because the policies were written on the last day of year one, we're going to assume that nothing is earned in year one, and instead, it's earned throughout years two and three.

So we take the premium written of 100, and we divide that by the coverage period of two years.

And that gives us net earned premiums of 50 in years two and three.

Now, in terms of claims expense, we're just going to take the expected loss ratio because we've been told the actual claims are as expected.

So we'll take the 84%, and we'll multiply that by the net earned premium for each year.

Now, clearly, that will give us no claims expense in year one, but it will give us 42 in years two and three, and you can see how we're matching the claims expense to the premium earned throughout the years.

Now, in terms of the claims paid, we've been told that 80% of claims are paid in the year after they're incurred, and clearly, that's going to be nil for year one.

For year two, we're going to take 80%, and we're going to multiply it by the prior year claims expense, which is nil for year one.

And that gives us nil for year two. But when we roll that forward to year three, you can see that claims paid were 33.6.

Now we've got all the ingredients that we need to calculate our claims reserves for each year. And we'll start off, as we always do, with the beginning balance being equal to the prior year ending balance, and that's nil.

Now we're going to add to that the claims expense for each year, and that's nil for year one.

And we're going to subtract from that the claims paid in each year.

And again, that's nil for year one.

So when we sum all those together, that gives us nil, and it doesn't look very exciting, but it is an important point to note that even though premiums have been written of 100, there's no claims reserves showing yet because no actual claims have been incurred.

Now let's roll forward these calculations for years two and three, and things should start to look a little bit more interesting.

And I think they do, because you can see that by the end of year two, the claims reserve is 42, and that reflects the fact that we've got claims expense of 42, but no claims have yet been paid. Then, by the end of year three, the claims reserve is 50.4 because we've added more claims expense, the 42, and we've deducted the 80% of the prior year claims that have been paid out. So you can see how the claims reserve builds over time as the claims come in and then they're paid out.