In the following chapter we’ll discuss again what the previous chapter said about the
premium calculation of traditional life insurance, but now we phrase the relations with the aid
of mathematical formulae.
All notation used in this chapter– with a few exceptions 
follow the actuarial standard
developed around the turn of the century, since here we are introducing the classical
premium calculation methods. Modern premium calculation methods will be discussed later,
in chapter 16.
1. Since the premium of the insurance is directly proportional to the sum assured
(disregarding the potential premium discount from the premium loading depending on the
level of the premium, that might be applied by some companies), it is enough to declare the
premiums.
2. Forint sum assured, and the premium of the actual sum assured can be
calculated very easily from this.
The base of the calculation is the life table. As we know, this shows the number of living at
age x from a starting population (generally 100,000 lives), as a function of age. In the
premium calculation we always start with the simplifying supposition that the number of
insured persons of age x, having an insurance of n years term is lx , according to the life
table.
3. This supposition doesn’t have any particular significant meaning, it only shows that
the risk community doesn’t consist of only one person.)
The basis of the calculation is naturally the equivalence principle, which here also means
that:
1. So if the number of insured in the starting year is lx, from which
2. the number of deaths during the first insurance year is dx,
3. the number of deaths during the second insurance year is:
4. Supposing 1 Forint sum assured the insurer’s liability at the end of year t is: 1
1 + −
⋅ x t
d
Forints. If we discount the expected payouts of the individual years to the beginning of the
insurance and add them up, we get the other side of the equivalence equation that we were
looking for:
5. Supposing payments at the end of the year results a little lower premiums than if we put the payments to the
middle of the year, since the liability of the insurer is due later. But the difference is not too big, and the effect is
somewhat compensated by the fact that payment usually doesn’t happen immediately at death, but generally 1-2
months later. The insurance company needs this time for the assessment of the circumstances of death and the
claim, and until that time the sum assured gains interest on the accounts of the insurer, for the insurer.
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