In this workout, we've been told that an insurance company has written a portfolio of insurance policies and receives the premiums on the last day of year one. Now we've been asked to calculate the unearned premium reserve at each balance sheet date for years one to three, and also the net premium earned during each year.

Now, the premiums written were 100 in year one, and remember, that was premium received on the last day of year one.

And no premiums were written in years two and three.

Now, in terms of the coverage period, it's a two-year coverage period.

So effectively, that means that the policies run from the last day of year one to the last day of year three, and that's going to be important to us when we're thinking about how the premium is actually earned.

So let's calculate the unearned premium reserve, and we start with our beginning balance for the reserve being equal to the prior year ending balance, and that's nil for year one because no premiums were written at the beginning of year one.

Now, we're going to add the premiums written in the year, and that's the 100 which was received on the last day of year one.

Now, we have to subtract from the unearned premium reserve any premiums actually earned in the year. But because this policy started on the last day of year one, the insurance company hasn't really earned any of the premiums yet.

So we're going to say that the premiums earned are nil in year one.

Now, we can sum all of those to give the ending balance for the unearned premium reserve, and that's 100, reflecting the fact that the 100 of premium actually received hasn't yet been earned.

Now, we can roll forward these calculations for years two and three, but we're going to need to do an extra little calculation to subtract the premiums earned in years two and three from that unearned premium reserve.

Now, to calculate this, we're going to take the premiums written of 100 in year one. I'm going to spread that throughout years two and three, which are the years when really they're earning that amount.

So, that gives us a premium earned in years two and three of 50 in each year.

And you can see that the unearned premium reserve has gone down from 100 at the end of year one to nil by the end of year three, and that's as the premiums are being earned, they're being released to the income statement.

Now, we can calculate our premiums, starting off with our written premiums of 100 in year one, and we can then deduct from that the change in the unearned premium reserve each year. So to do that, we're going to take our prior year ending balance, and we're going to deduct from that the ending balance for the following year. And that gives us a change in the unearned premium reserve of 100.

Now, if we sum that together with the written premiums, that gives us a net earned premium of nil for year one, because remember, we haven't actually earned any premium in year one.

Now, we can roll forward these calculations for years two and three, and you can see that even though the written premium was nil in years two and three, the unearned premium from year one is being released.

So that gives us a net earned premium of 50 in each of years two and three.