In this workout, we've been given information on the investment returns and account value for a unit linked policy. We've been asked to calculate the insurance company's profits over the policy life assuming the policy holder dies at the end of year eight. Now, here you can see the investment returns for each year from years one to eight and also all the information on the account value. Now, one thing we're gonna have to calculate is the policy holds investment returns. Now you can see that the premiums and the cost of insurance both BOY which means they occur at the beginning of the year, so we'll need to include those when we're calculating our investment returns. Whereas the asset management charges and the amounts paid to policy holders are EOY which means they occur at the end of the year. So we're gonna exclude those. So we'll take our annual rate of return and we'll multiply that by the beginning value plus the premiums less the cost of insurance charged to the policy holder. So we can roll forward those calculations and that gives our investment returns to the policy holder for each year from years one to eight. Now, the final thing we need to do is just sum all of the information above to give the ending balance on the account value for each year from years one to eight. And you can see that in year eight, that account value goes down to nil reflecting the fact that the policy holder has received their benefits on death. Now, the first thing we're gonna need to do in terms of calculating the profits is to calculate investment returns. So we need to know what the cash balance is for the insurance company. So our beginning cash balance is equal to our prior ending cash balance. Now we're gonna add to that the net cash flows from the insurance company's perspective and that's clearly gonna be the premiums received less any amounts paid out to the policy holder. But because the policy holder only receives their money at the end of year eight, we actually don't need to worry about that when we're calculating our investment returns. So we'll take the premiums of 100 and now add that to the cash balance, and we can then use our rate of return of 6% and multiply that by the beginning cash balance plus the net cash flow. So that gives investment returns of six in year one. And then we add all of that together to give the ending cash balance. Now let's roll forward our calculations to the end of year eight. And you can just see that the investment returns of the insurance company are slightly higher than the policy holders investment returns. There's a spread there, and that reflects the fact that the policy holder is charged things like the cost of insurance charges and also asset management charges which lowers the amount that they will accrue investment returns on. So now we've calculated investment returns, we can calculate the operating profits from the policy and we'll start off with the fee income which is all the amounts deducted from the account value. So that's the cost of insurance charges and also the asset management charges. Now we can add to that the investment income for the insurance company. So remember that's not the policy holder's investment returns. Now we need to deduct from this the benefits expense but because this is an investment type policy it's not going to be the change in reserves and the benefits paid this time, it's just gonna be the amounts credited to the policy holder's account value. So we can just take that from above and then we can sum all of that to give the operating profits to the policy. So let's roll forward those calculations to the end of year eight, and that shows the operating profits throughout years one to eight. And that's really a function of the fee income, which is deducted from the policy holder and also the spread on the insurance company's investment returns versus those of the policy holder.