In this workout, we've been told that a unit linked insurance policy offers a death benefit based on the policy holder's account value but with a guaranteed minimum death benefit. Now, the premiums paid the cost of insurance and the investment returns are set out below and asset management charges are 1%. Now, we've been asked to calculate the death benefit payable if the policy holder dies at the end of year eight and reassuming that premiums are paid at the start of each year and benefits are paid at the end. Now the guaranteed minimum death benefit is 200 and that means that even if the account value falls below that because of say poor investment returns, the policy holder would still receive 200 on their death. Also, the asset management charges are 1% and these are charged at the end of the year, EOY, meaning end of year. Now, we've also been told what premiums are paid each year and you'll see here that they vary each year, which is normal for a unit linked policy as long as the premiums exceed a certain minimum amount. Also, we've been told the annual investment returns which vary each year because that will depend on market conditions. Finally, we've been told the cost of insurance charges which are deducted from the account value at the beginning of each year, BOY, meaning beginning of year and you can see that these charges increase each year and they reflect the cost of providing the guaranteed minimum death benefit. So let's now calculate the account value for each year because we'll need to do this to work out what the account value and therefore, what the potential death benefit is for the end of year eight. Now we start with our beginning value being equal to the ending value for the previous year and then the premiums we can simply take from the schedule above of 100 in year one. And the cost of insurance charges. We can also take from above. Now the investment returns. We can calculate using the rates given above but we need to multiply that by the account value before any asset management charges are levied. So we simply take the beginning account value plus the premiums less any cost of insurance charges and that gives us that investment return. Next, our asset management charges, we know that they're 1% and we can multiply that by the account value at the end of each year, which is our beginning amount plus the premium, less the cost of insurance charges plus any investment return. So that gives us an asset management charge in year one of one. Now the ending account value is just the sum of all those items, and we can then roll-forward this calculation to the end of year eight, giving an account value at the end of year eight of 814.7.

Now the death benefit is gonna be the higher of the guaranteed minimum death benefit of 200 and the account value of 814.7. Now we're gonna use a max function to put that in formulaically, so it's the max of our guaranteed minimum death benefit and our ending account value, giving a death benefit at the end of year eight of 814.7.