# How to Calculate an Actuarial Reserve

This isn’t as complex as it might sound. Firstly; it’s probably a good idea to define what an actuarial reserve actually is. So:

An actuarial reserve is used to account for the amount of money that an insurance company will be liable to pay (in the event of a claim) based on an estimate of the present value of all future income that is derived from a contingent event.

What does that mean? It means in essence that we add up all the money that’s due on a claim from a policy. We work out what that money is worth in today’s terms (present value). Then we look at how much we have to invest in order to meet the claim’s future value.

## Calculating Actuarial Reserves

In order to calculate an actuarial reserve we need to make some simple assumptions; these involve how much we are likely to have to pay out and how much interest we can earn on our investments. The more accurate our assumptions – the better our actuarial reserves can be calculated. This is not always a simple task and in most cases a certain level of error can be expected.

Let’s say that we expect to pay out £500,000 on a policy and that we expect to pay out £250,000 in Year 1, £150,000 in Year 2 and £100,000 in Year 3.

The actuarial reserve should tell us how much money we need to put aside today to cover these payments.

Now £1 today is worth more than £1 in 3 years’ time. (If you don’t believe this – how much did a pint of milk cost when you were 6? How much does it cost today? A pound won’t buy anywhere near as much milk now as it did then – money decreases in value over time thanks to many factors including inflation).

So in order to make for an insurer to make provision for these payments they need to determine what they need to invest today – to pay out in full when the payments are due.

There is a reasonably simple formula to do this:

Amount Required to be Paid x (1+the rate of interest)^-years=The Amount Required to be Invested

Now this may look complicated but if we assume the rate of interest to be a steady 6% on our investments the example above can be worked out like this:

In Year 1 we need to pay £250,000 so let’s put the numbers into the formula:

250,000 x (1+0.06)^-1= £235,849

That means if we put £235,849 into our investment vehicle now; in 1 year it will be worth the £250,000 we need to pay out.

In Year 2 we need to pay £150,000 so:

150,000 x (1+0.06)^-2=£133,499

And investing £133,499 now at that 6% will realize £150,000 in 2 years’ time when we need to pay out.

In Year 3 we need to pay £100,000 so:

100,000 x (1+0.06)^-3=£83,961

## Calculating the Actuarial Reserve of a Policy

The actuarial reserve is simply a sum of all the amounts that we need to invest today in order to meet our obligations under the policy.

So in the example above this £235,849 + £133,499 + £83,961 = £453,309 is our actuarial reserve.

If we invest this amount of money and get a 6% interest rate; it will be worth the full £500,000 we have to pay to meet our obligations under the claim on the policy.

## Calculating the Actuarial Reserve of an Insurer

If you want to calculate the actuarial reserve of an insurer; you simply calculate the actuarial reserve of each policy and then add them all together.  