TEMPORARY LIFE ANNUITIES

Life annuities may be either temporary life annuities or whole life annuities. Both kinds have many practical uses in actuarial calculations. In a temporary life annuity, each payment is made only if a designated person is then alive, but the payments are limited to a fixed number of years. In a whole life annuity, the payments continue for the entire lifetime of a designated person.

PROBABILITIES INVOLVING MORE THAN ONE EVENT

Probabilities involving more than one event may be calculated using the Addition Rule and Multiplication Rule. Those are as follows:

PRESENT VALUE OF A LIFE ANNUITY

As stated earlier, an annuity is a series of payments and the present value of the annuity is the total of the present values of each of the individual payments. To find the present value of a series of payments where each payment is made only if the designated payer or recipient is alive to pay or receive it, we can now use the method for calculating the present value of a single payment.

For Example: The present value at age 35 of a life annuity of $100 per year for three years (with the first payment due at age 36) can be represented by the following line diagram:

LIFE ANNUITIES

In this topic, you will begin to learn how life insurance companies make important calculations which combine the principles of compound interest and probability. In a life insurance company, annuity contracts represent payments being made only if a person is alive, while life insurance contracts represent payments being made only when a person dies. We will explain how to calculate the present value and the accumulated value of life annuity payments, that is, payments which are contingent on a designated person being alive.

Present and accumulated values for life annuities can be calculated in a manner quite similar to the method for annuities. We will begin by considering the present value and accumulated value of a single payment.

THE CENSUS OPERATION

In any country census is conducted within the frame work established by registration. Whether a census covered the entire population of a nation or on the some segments there off, it involve the following step.

DEMOGRAPHY

Demography is the science of human population. A Belgian name of ACHILE GLUILLARD first used the term in 1855 when he published his book in FRENCH named “Elements of Human Statistics or Comparative Demography”. He defines it as the natural and social history of the human species or the mathematical knowledge of population, of their general changes and of their physical civil intellectual and moral conditions. Population analysis is more or less used as synonymous to demography. However population analysis has more mathematical and numerical analysis. The term demography has been derived from two Greek words DEMOS meaning to human population and GRAPHY means to measured. Demography has further defined in different senses and levels. We have narrowest sense, broadest sense and widest sense.

PROBABILITIES OF DYING

The probability that one of the events will happen is the total of the probabilities of each individual event happening.

(Probability of living 1 year) + (Probability of Dying Within 1Year) = (Probability of Either Living or Dying That Year)

Symbols can be substituted for each of the above expressions, as follows:

Substitute p_x for (Probability of Living 1 Year)

Substitute q_x for (Probability of Dying within 1 Year)

Substitute 1 (certainty) for (Probability of Either Living or Dying That Year)

Consequently, the equation is