LIFE INSURANCE MATHEMATICS 17

present value of the chance of having to pay the claim then is $942.60 multiplied by .00746.

Proceeding in this manner, we find that the present value of the chance of paying the claim at the end of the fiftieth year is .02321 (since of the 100,000 setting out at age 10 2,321 die in their sixty-ninth year of age) multiplied by $228.11, the present value of $1,000 if paid at the end of 50 years. Similarly, .00001 multi-plied by $78.70 is the present value of the chance that a claim will fall due 85 years from now, be-cause of the possible survival of a given one to the age of 95 and his death in that year of age.

When you add all these present values together, you have the present value of all the chances that $1,000 will be paid on account of the death of the insured. To put it another way, you have the present value of the premiums on an increasing scale which he would need to pay throughout his lifetime, multiplied in each case by the probability that he will survive to that age to pay the premium. The result is the single premium, which will pay for his life insurance as long as he lives.

In paying for this insurance out of the single premium you may look at it in either of two ways, namely :

First: That each year so much of the interest upon the single premium, and of the single premium itself, if necessary, is taken as is required