So in this workout, we've been told that a customer has taken out a whole life insurance policy with premiums, benefits, and policy charges all detailed below, and the cash value is based on an interest rate of 4%. Now, we've been asked to calculate the surrender value if the policyholder surrenders their policy at the end of year eight.

Now, the annual premium is 100, the guaranteed death benefit is 1,100, and the interest crediting rate, that's the amount used to calculate the cash value, is 4%.

Now, we've also been given some information on cost of insurance charges.

So what on earth are these? Well, these reflect the cost to the insurance company of providing the guaranteed death benefit, and they are deducted from the cash value each year at the beginning of the year, BOY. So these charges are equivalent to the cost of providing a one-year term life insurance policy each year to the policyholder, and you can see that this cost increases each year with the increasing mortality risk. Now, we've also been told what the surrender fees are, and these surrender fees are deducted from the cash value if the policy is surrendered in its early years.

So these fees seek to deter the policyholders from an early surrender, and you can see that these fees decrease each year.

In fact, by year eight, they're nil.

So to calculate the surrender value at the end of year eight, we need to know what the cash value is at the end of year eight.

So let's calculate that now. And we start off with the beginning cash value being equal to the ending cash value for the previous year. Now, the premiums we can take from our information above, and that's our annual premium of 100. The cost of insurance, we just need to take from the schedule above, and we can now calculate the interest credited, which we know is 4%, and we're going to multiply this by the sum of our beginning cash value, plus our premium, plus our cost of insurance, all of which occur at the beginning of the year.

And then we can now calculate the ending cash value as the sum of all of those items. So actually to then calculate the cash value at the end of year eight, that's pretty straightforward because we just need to roll forward all of these calculations. And you can see that the cash value for the end of year eight is 763.7. And because we know the surrender fees are nil, we can simply take the surrender value as being equal to the cash value at the end of year eight. Now, an important thing to note is that if the policyholder had in fact died at the end of year eight instead of actually surrendering their policy, they would have received 1,100.

So you can see that actually this guaranteed death benefit is equal to the surrender value or the cash value of 763.7, plus an amount of 336.3, which reflects the additional cost of insurance for the guaranteed death benefit.