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Rate-Making Premiums Payable More Frequently than Annually

RATE-MAKING PREMIUMS PAYABLE MORE FREQUENTLY THAN ANNUALLY. Premiums are sometimes payable more frequently than once a year; for instance, semi-annually, quarterly, bi monthly, monthly, or even weekly.

It would be possible, of course, by extending the prin ciples already laid down, to compute net premiums pay able in this manner. All that would be requisite would be to divide the net single premiums by the present value of a life annuity of $i per annum, payable (in equal parts in advance) two, four, six, twelve or fifty-two times a year, as the case may be, instead of by the present value of a life annuity due of $1. But, unless payable weekly, or sometimes monthly, premiums are not usually dealt with in this manner. The policy usually contains a provision that, in event of death during the year, premiums for the year, not yet paid, are to be deducted from the claim. This transforms the insurance into one with annual pre miums payable in instalments.

On this basis it is customary to make an arbitrary addi tion to the gross annual premium and divide it, thus in creased, into the desired number of parts. The following are the usual rules : For semi-annual premiums, add 4 per cent. of itself to the gross annual premium and divide by two.

For quarterly premiums, add 6 per cent. of itself to the gross annual premium and divide by four.

For bi-monthly premiums, add 8 per cent. or io per cent. of itself to the gross annual premium and divide by six.

84 For monthly premiums, add 20 per cent. of itself to the gross annual premium and divide by twelve; or divide the gross annual premium by ten, which gives the same result.

There is no rule as to weekly premiums, which are usually based upon true net weekly premiums. The mor

tality table employed in computing net weekly premiums and sometimes monthly premiums as well is sometimes different from the mortality table employed in com puting net premiums for ordinary insurances, because the lives are not upon the average so good.

The greatest part of the increase over the annual pre mium, made in computing premiums payable more fre quently, is to cover the added expense. Thus, upon the basis of 4 per cent. interest, the following rates of increase only would be necessary to make good the interest lost by deferring the receipt of part of the premiums : Semi-annual : 2 per cent. on half the annual premium due in six months, equal tot per cent. on the annual premium.

Quarterly: 3 per cent. on one-fourth of the annual pre mium, due in nine months, 2 per cent. on one-fourth due in six months, and i per cent. on one-fourth due in three months equal to 11 per cent. on the annual premium.

Bi-monthly : 31 per cent. on one-sixth of the annual premium due in ten months, 21 per cent. on one-sixth due in eight months, 2 per cent. on one-sixth due in six months, I1 per cent. on one-sixth due in four months, and per cent. on one-sixth due in two months, equal to If per cent. on the annual premium.

Monthly: 31 per cent. on one-twelfth due in eleven months, and so on down to 1 per cent. on one-twelfth due in one month, equal to i% per cent. on the annual pre mium.

Weekly : About 2 per cent. on the annual premium.

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