Premiums Paid at Intervals of Less than One Year

By an extension of the principles laid down heretofore in computing single and annual premiums, it would now be possible to ascertain weekly, monthly, quarterly, and semi-annual premiums. It would be necessary to make the time unit the proper fractional part of a year instead of one year. The difficulty with this method lies in the fact that none of the mortality tables in existence are graded for periods of less than one year. To illustrate, it is impossible to determine from any of the tables in use the probability that a man arriving at age 25 will die within one week, one month, or six months. We can only say that the chance that he will die within one year equals 718/89032. Because of this fact the true weekly, monthly, or quarterly premium cannot be ascertained, and some method of approximation to the correct result must be used. The usual method is to make a percentage addition to the annual premium, more or less arbitrary in amount, and then divide this result into the requisite number of parts. By this plan the premium is looked upon as an annual premium paid in installments. That is, at the beginning of any policy year the entire premium for the policy is considered to be due and payable, but the insured is given the privilege of paying it in installments; then if the contract should mature by death before the total installments for the year are paid, those remaining still due will be deducted from the matured value of the policy and the balance only will be paid to the policyholder. Thus, a policy for $1,000, being paid for by quarterly premiums of $10.00, might mature by death shortly after the payment of the first $10.00 installment of the year's premium. The beneficiary under the policy would, therefore, be required to pay the three remaining installments of $10.00 each before receiving the proceeds of the policy, or this would be equivalent to the settlement of the claim in force by the payment to the beneficiary of $970.00.

The percentage added to the annual premium to obtain the semi-annual premium varies with different companies. Some add 2 percent, some 2½ percent, 3 percent, or even 4 percent. Thus one company quotes a gross annual premium on an ordinary life policy, age 45, of $37.08. Adding 2 percent, of this amount, or $.74, gives $37.82, and this result divided by two equals $18.91, the semi-annual premium quoted in this company's rate book. Another company quotes an annual premium of $37.57 for the same policy and a semiannual premium of $19.54. This latter figure is obtained by adding 4 percent, and dividing by two. The same method is used likewise on twenty-payment life policies. At age 45, the annual premiums of the two companies referred to are respectively $45.73 and $45.30. If 2 percent, be added to the first and 4 percent, to the latter and these results be divided by two, the amounts obtained for the semi-annual premium will be respectively $23.32 and $23.56. These are the quotations found in the rate books.

The same method is used in computing quarterly, bimonthly, or monthly rates, of course varying the percentage added in each case. The rate books do not ordinarily quote bi-monthly or monthly rates. From 4 to 6 percent, is usually added to the annual premium and this result divided by four to obtain the quarterly premium. Thus to the annual rate of $37.08 quoted above for an ordinary life policy is added 4 percent, or $1.48, making a total of $38.56 and this sum divided by four gives $9.64, the quoted rate for quarterly payments.

The increase in the rate on premiums paid more frequently than annually is justified on three grounds: (1) the greater expense of collection, where collection must be made two, four, or more times yearly instead of only once; (2) the loss of interest, due to the assumption made in computing annual premiums that the premium is paid in at the beginning of the year and draws interest until paid out at the end of the year. On the basis of a 3 percent, interest assumption in computing premiums the interest lost in case of semi-annual premiums will be 3 percent, on one-half of the annual premium for a period of six months. (3) Some of the companies justify this increased rate because of the greater tendency to lapse policies where premiums are paid twice or four times yearly instead of only once. The temptation to lapse comes twice or four times a year likewise, and thus results in a greater lapse ratio among these policyholders than in the case of those who pay annually.