In this workout, we've been told that an insurance company has written a portfolio of term life insurance policies, and we've been asked to use a net premium approach to calculate the insurance provisions over the portfolio life. Now, for simplicity, we'll assume that all cash flows occur at the end of each year, and that includes the premiums. Now, the premiums and expected benefit payments are given from years one to eight, and we've also been told that the insurance company expects to generate a return of 5% on their investments. And we'll use that for our discount rate. Now, we've also been told that the provision for adverse deviation is 10%, so that's the buffer that needs to be built into the reserves. So we're gonna use that to adjust our discount rate. So we'll take our discount rate and multiply it by one minus to 10%, and that gives us a slightly lower, more prudent discount rate, reflecting the fact there's inherent uncertainty in those cashflow forecasts. Now, we can use that adjusted discount rate for our net premium ratio, which is the present value of the benefit payments divided by the present value of the premiums. Now, we use the NPV function for that calculation. So that's the discount rate and then the cash flows. And remember that the NPV calculation assumes that the first cash flow is one year away. And that's fine, because the question tells us to assume that. And that gives us a net premium ratio of 94.2%. And what that's telling us is basically that out of the premiums that the insurance company receives, 94.2% of those are to cover the benefit payments, and the remaining 5.8% is their profit. So we can use that net premium ratio and multiply it by the premiums for each year. And that gives us the amount of net premium. It's the amount of premium received each year, which will cover the expected benefit payments. Now, we can calculate our insurance reserves using that information and ordinarily, we would assume that our insurance reserves are nil at the start of the policies. But we are actually gonna do a little calculation just to check that, 'cause we know that the reserves should be equal to the present value of the benefit payments less the present value of the net premiums. So again, we're gonna use that NPV function. And this time, I'm gonna lock all my cell references.

So we'll take the benefit payments. We'll lock that final reference.

And we'll deduct the present value of the net premiums.

So that gives us a nil balance for the insurance reserves at the start of the policies. And that's good because we know that the present value of the net premiums are set so that they're equal to the present value of the benefit payments. Now we can use that as our beginning balance in the next year. Now the benefits paid and change in reserves, that's gonna be our residual in this calculation. So I'm gonna leave that, but we will then deduct the benefit payments from above. And the ending balance on the reserves, we can just roll that forward from our prior calculation. And that's 113.1, reflects the net premium flowing into the reserves for that year. Now, the benefits paid and change in reserves, we can just calculate.

And that 113.1 is what we'll be showing as our claims expense on the face of the income statement. Now, let's roll forward all our calculations, and we'll do that to the end of year seven, 'cause that's when things stop happening. And you can really see how the reserves evolve over time, starting off at nil and then building as the net premiums flow into the reserves. And then they start to reduce again as the benefits are paid, ending up with a nil balance on reserves by the end of year seven.