Banking and Insurance · Ch 4 — Life Insurance and Other Insurances
Computation of Premium and the Mortality Table
Computation of Premium and the Mortality Table
The premium is the price the policyholder pays for the cover. Fixing it fairly is the central problem of life insurance: it must be high enough to let the insurer pay all the claims that will arise and meet its expenses, yet low enough to be reasonable to the policyholder. The premium is not guessed — it is calculated from three main factors.
The three bases of the premium
- The rate of mortality — how likely a person of a given age is to die within the year. This comes from the mortality table.
- The rate of interest — the premium is received in advance and invested, so it earns interest before the claim is paid; a higher assumed rate of interest reduces the premium needed.
- Expenses and contingencies (loading) — the insurer's costs of management, agents' commission and a margin for safety are added on. The premium after adding these is the office (gross) premium; before adding them it is the net (pure) premium.
The mortality table
A mortality table (or life table) is a statistical table, prepared from the recorded experience of a very large number of lives, showing at each age how many out of a starting group are expected to be living and how many are expected to die during the year. Its typical columns are:
- Age (x)
- Number living at that age (lₓ)
- Number dying during the year (dₓ) — where dₓ = lₓ − l(next age)
- Rate of mortality (qₓ = dₓ ÷ lₓ) — the probability that a person aged x dies within the year.
A short illustrative extract (figures assumed, for teaching only) is shown below:
| Age (x) | Number living (lₓ) | Number dying (dₓ) | Rate of mortality (qₓ = dₓ ÷ lₓ) |
|---|---|---|---|
| 30 | 100,000 | 200 | 0.00200 |
| 31 | 99,800 | 220 | 0.00220 |
| 32 | 99,580 | 240 | 0.00241 |
| 33 | 99,340 | 265 | 0.00267 |
Reading the table: of 1,00,000 persons alive at age 30, about 200 are expected to die before reaching 31, so the chance of a 30-year-old dying within the year is 200 ÷ 1,00,000 = 0.002, i.e. 2 in a thousand.
How the premium is built from the table
- The simplest premium is the natural (risk) premium for one year's protection. Ignoring interest and expenses, the pure premium each life must contribute for one year equals the rate of mortality × sum assured, because the total so collected exactly meets the expected claims of those who die that year. …
A statistical table showing, at each age, how many of a large starting group are expected to be living and how many to die during the year; the bas …
The probability that a person aged x dies within the year, equal to the number dying divided by the numb …
An equal fixed premium charged every year of the term; higher than the risk cost in early years and lower in later years, the excess being a …
The net premium covers only mortality and interest; the office premium adds loading for expenses and contingencies and is what the pol …