In this workout, we've been told that an insurance company has written an insurance policy and we've been asked to calculate the profits generated in the year from this policy. Now we've been told that the premium written was 100. Now this means that the premium received by the insurance company was 100. We've also been told that the loss ratio was 70%, and this means that the claims against the policy was 70% of the premium written. We've also been told that the coverage period was one year. So we're calculating the profits generated from the whole of this policy. Finally, we've been told that the investment return that the insurance company can generate is 10%. So let's calculate the profits from this policy, remembering that this is gonna be both the underwriting profit and also an investment return on the premiums. So starting off with the premiums we know that their premiums received were 100 and this is effectively the revenue generated by the insurance company. But against this, we know that there were some claims against the policy, and this is effectively an expense. So we're gonna take the loss ratio of 70% and multiply that by the premiums written, and that gives a claims expense of 70, and together the premiums, less the claims expense, gives our underwriting profit of 30. So that's a nice healthy profit from the underwriting activities. But that's not all because we know that the insurance company can invest the premiums until the claims are paid out to generate an investment return. So we also know from the question that the claims are paid out at the end of the coverage period. So effectively, the insurance company can invest all of the premium of 100, and generate an investment return of 10% on that to generate an investment return of 10. So the total profit from this policy is the underwriting profit of 30 plus the investment return of 10 to give a total profit of 40.