Cash Surrender and Loan Values for later years will be computed upon the above The Loan Values in the above table are the maximum amounts available at the 15.. MODES OF SETTLEMENT UPON DEATH OF INSURED. If there be no existing assignment of the Policy made as herein provided, 10445 (1) By the payment of interest at the rate of three per centum of Unless otherwise specified by the Insured or by the beneficiary in mak- The above Modes of Settlement are based upon an assumed interest The above Modes of Settlement are not applicable if the beneficiary PAGE 3 OF POLICY New NOTE.-No change, designation, or declaration shall take effect until endorsed on this Policy by the Company at the Home Office. REGISTER OF CHANGE OF BENEFICIARY. ENDORSED BY ENDORSED BY the Home Office. REGISTER OF CHANGE IN MODE OF PAYMENT OF PROCEEDS UNDER THIS POLICY. NOTE.-Changes of mode of payment and revocation of any change, must be requested in writing and shall not take effect until endersed on this Policy by the Company at The provisions of this Policy will be found to be exactly the same as those of the Ordinary Life except (1) that the annual premium is $383.40, instead of $281.10, and that instead of being paid annually during life it is to be paid every year during the continuance of the Policy until premiums shall have been paid for twenty full years, or until the prior death of the Insured; (2) that the amounts of cash surrender and loan value and of paid-up insurance in the Table on page 3 are larger in this Policy, and that the time for which the insurance will be continued,-in case the payment of premiums is discontinued after two years' premiums have been paid-, is longer. We will now examine into the reason of this. THE PREMIUM AND THE LOADING. It will be noted that this Policy insures during the whole period of lifejust as the Ordinary Life Policy does-the present value of the net premiums to be received must therefore be the same as in the former case and these values are obtained in the same way. The only point that need be discussed here is how the Company may realize these values in twenty years. The present value of the insurance costs of $1,000 insurance taken at age 35 or the net single premium, in that case was found to be $419.883. In order to get the equivalent of this in equal annual payments from the living from age 35 to age 55 we first find the present value of $1 paid by each person living according to the Mortality Table during the twenty years beginning at age 35. We begin with $1 each from the 81,822 persons living at age 35, or $81,822. At the end of the first year $1 would be received from each of the 81,090 persons then living, and this $81,090 would be discounted at 3% for one year. In the same way the amounts to be received at the beginning of the years following would be discounted until twenty payments of $1 each had been made. If we performed these operations and added together the amounts thus obtained we should have a total of $1,150,932.798, which is the present value of $1 each received in cash from 81,822 persons living at age 35 and of $1 each annually thereafter from the living until twenty payments have been made.* But we must have present values equal to 81,822 x 419.883 or $34,355,666.826; therefore we must have from each person annually for twenty years as many dollars as 1,150,932.798 is contained times in 34,355,666.826. Performing the division gives 29.85; therefore the net annual premium to be paid for twenty years is $29.85 per $1,000. As the gross premium charged in this Policy is $38.34 per $1,000, the loading is $8.49. The Ordinary Life loading is $7.03 or 33 1/3% of the net. This net premium is the Ordinary Life net premium plus $8.77, which-with its loading -is called the "higher premium element". If we deduct the Ordinary Life loading from $8.49 we have $1.46, which is 16 2/3% of $8.77. In other words the loading on the higher premium element is at one-half the Ordinary Life rate. *If we divide $1,150,932,798 by 81,822 the quotient will be $14.06624, and this is the present value of $1 in cash and $1 per annum during nineteen years or until prior death, from persons beginning at age 35. This is called the present value of a "Temporary Annuity Immediate" during the period of twenty years. Tables have been constructed showing the present value of a "Temporary Annuity Immediate", beginning at any age and continuing during any desired period. Knowing what it means and how it is obtained, we may hereafter take these values from such a table. VERIFYING THE RESERVES. If we were to construct a table after the manner of the table on page 108 we should have in the last column the amount of reserve on hand for each $1,000 insured at the end of all the years following age 35. These amounts for the first ten years would be as follows, omitting fractional parts of a dollar : While we have taken these figures from a Table of Terminal Net Values, they may easily be verified. For example, At the end of the twentieth year the Insured will all be age 55 and their policies will all be paid in full, there must then be on hand for each the net single premium for age 55; and the reserve at the end of each year thereafter will be the net single premium for the attained age. The reason is obvious; the net single premium is the amount of cash in hand at any age which will pay all death-losses under policies issued at that age; those who insure under a twentypayment life policy at age 35 and pay premiums for twenty years will pay no more, but are now insured for life and will remain so. Hence at the beginning of each year thereafter they will be in the same position as that of men newly insured by the payment of the net single premium. We have seen how the cost of an insurance for the whole life may be paid for by twenty annual payments-simply by making the present values of those payments equal the present value of the insurance. In a similar manner we may arrange to collect these values in any specified number of years. Limited-Payment Life Policies are accordingly issued which are paid up by either five, ten, fifteen, twenty, twenty-five or thirty annual premiums. EFFECT OF THE LARGER RESERVES. We will now examine the Table of Loan and Surrender Values on page 3 of the Policy. If we compare the figures in Column 1 with the reserves already given we shall have the following, omitting fractional parts of the dollar: The cash value at the tenth year and thereafter is the full reserve, omitting fractional parts of the dollar. As we have observed in considering the Ordinary Life Policy, the law does not require a surrender value of any kind until three years' premiums have been paid; the company allows approximately one-half of the reserve as such value after two years' premiums have been paid under the Ordinary Life Policy and 66% under this Policy. The surrender charge under each Policy at the third year is approximately 20% of the reserve and diminishes until it reaches nothing at the tenth year. The decline is however more rapid under the higher premium Policy, for the reason that the reserve is larger in proportion to the insurance. The surrender charges have the following ratios to the reserves : If we compare these surrender charges both with respect to the amount per $1,000 insured and the percentage of the reserve, with the surrender charges allowed by law-as we did those of the Ordinary Life Policy-we shall find they are always smaller than the legal allowances. The only point requiring special explanation is the manner of ascertaining the surrender charge under the Massachusetts law, which is "5% of the present value of all the net premiums which by its terms the Policy is exposed to pay." At the end of three years "The Policy is exposed by its terms to pay" net premiums of $29.85 for 17 years, hence we must use for the multiplier not the present value of $1 paid annually during life-as in the case of the Ordinary Life Policy-that is to say the "Annuity Immediate"-nor the present value of $1 paid during twenty years or until death, if prior, that is the "Temporary |