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4. My ship Keystone State is valued at $ 35000, and her cargo at $ 75000. I procure an insurance on f of the value of the ship, at 3£ per cent., and on § of her cargo, at 2£ per cent. What is the amount of premium? Ans. $1932.50.
5. My library, worth $3675, I got insured by paying 4£ per cent.; and the policy cost me $1. The library having been destroyed by fire, what was my actual loss? Ans. $ 180.15$.
6. The premium for insuring $ 9870 was $ 690.90. What was the rate per cent.?
7. White & Bigelow effect an insurance on their store and goods, worth $ 47600, for 5 years. The first year they are to pay 4£ per cent.; the second year, 3J per cent.; the third year, 4f per cent.; the fourth year, 5 per cent.; and the fifth year, 5£ per cent. What is the whole they are to pay for the insurance? Ans. $ 11,007.50.
446i To find what sum must be insured, at a given rate, to cover both property and premium.
Ex. 1. For what sum must a policy be taken out, to cover both property and premium, the value of the property being $ 2475, and the rate of insurance 10 per cent.?
$ 2475 -r- .90 = $ 2750.
Since the sum to be covered by the insurance includes both the property and the premium, and as the premium is 10 per cent., or .10 of that sum, the property, evidently, must be .90 of the sum for which the policy is to be taken out.
Rule. — Divide the value of the property to be covered by 1 decreased by the rate of insurance expressed decimally, and the quotient will give the whole sum to be covered.
Note. — When the rate of insurance and premium are known, the amount insured may be found by Art. 350.
2. A manufacturing company own a factory valued at $ 26250. For what sum must a policy be taken out to cover the property and premium of insurance, the rate being 12£ per cent.? Ans. $ 30,000.
3. A store and its goods are worth $ 6370. What sum must be insured, at 2 per cent., to cover both property and premium? Ans. $ 6500.
4. The premium for insuring a school-house, at the rate of 1^ per cent., was $ 50. For what sum was it insured?
Ans. $ 4000.
5. If a policy covering property and premium be taken for $ 600, at 10 per cent., what is the value of the property covered? Ans. $540.
6. A merchant adventured $1000 from Boston to New Orleans, at 3 per cent.; thence to Chili, at 5 per cent.; thence to Canton, at 6 per cent.; and thence to Boston, at 7 per cent. For what sum must he take out a policy, to cover his adventure the voyage round? Ans. $ 1241.348.
447. Insurance on life is a contract which stipulates for the payment of a certain sum of money on the death of one or more individuals, in consideration of an immediate payment, or an annual premium, being made by the insured.
A temporary insurance on life is a contract to pay a certain sum in case a given individual dies within a given number of years.
448. The amount of premium required of the insured as a security for the payment of a certain sum at his death by the insurer, is based upon the expectation of life of the insured, and on the rate of interest or net profit the insurer may be able to make by investing the premium.
449. By expectation of life is meant the average number of years of life that remains to any individual of a given age, as determined by the rates of mortality.
450. The Carlisle Table of the Expectation of Life, which is in general use in England, has also been taken as a guide by some American companies in fixing their rates of insurance.
Other companies have been guided in fixing their premiums by a table prepared by Dr. Wigglesworth, with a special reference to mortality in this country, and which the Supreme Court of Massachusetts has adopted as a rule in estimating the value of life estates.
451. The expectation of life. according to the Carlisle Table and according to that prepared by Dr. Wigglesworth, is shown in the following
Against any age given in the table may be found the expectation of age corresponding to it.
452. The transactions of life insurance companies extending as they do over a term of years, the value of money and the average rates of interest, no less than the expectation of life, have an important influence in fixing their rates of insurance.
153. The premiums of life insurance are generally reckoned at a certain sum on $ 100, payable annually in advance.
The rates of annual premium for insuring a healthy life for one year, for seven years, or for the whole period of life, in the sum of $100, by the Massachusetts Hospital Life Insurance Company, of 15oston, and by the Girard'Life Insurance Annuity and Trust Company, of Philadelphia, are given in tha toilowing
According to the table, a healthy man who is 42 years old next birthday, by paying the Massachusetts Hospital Insurance Company $, 1.31, would secure to his family, heirs, or to whomsoever he desires, $ 100, should he die in one year, and in the same proportion for a larger sum. And if he would obtain a life insurance of the Girard Life Insurance Annuity and Trust Company, he must pay annually $ 3.40. The New York Life Insurance Company has a schedule of rates like that of the Girard Company, given in the table.
454. To compute the premium of life insurance for any given amount.
Ex. 1. What premium will the Massachusetts Hospital Life Insurance Company require for the insurance of a life one year for $ 1728, the person being thirty years of age next birthday? Ans. $17.45.
Operotion. By the table we find the
$ 1 7 2 8 X .0 1 0 1 = $ 17.45. premium on $100 to be $1.01.
Therefore $$=If-J = * 0101 = the premium on $ 1 for one year, and $ 1728 X .0101 = the premium on $ 1728 for the same time. Hence,
Compute the premium on the sum to be insured at a rate proportionate to the given premium on $ 100.
2. What amount of premium must S. C. Kendall pay annually to the Massachusetts Hospital Life Insurance Company, to effect an insurance on his life for 7 years for $8000, his age being 33 years? Ans. $ 91.20.
3. Robert Vaux, 60 years of age, wishes to engage in a very profitable speculation; and being obliged to borrow the necessary funds, he effects an insurance on his life for 7 years, for S 78000, at the office of the Girard Life Insurance Company. Required the amount of the annual premium. Ans. $ 3829.80.
4. What will be the yearly premium for insuring a person's life, who is 15 years old, for $ 2000 for 7 years, at the New York Life Insurance Company?
5. A gentleman 45 years of age, being bound on a long and dangerous voyage, and wishing to secure a competence for his family, obtains an insurance for life of the Girard Life Insurance Company, for $ 12000. By an act of Providence he dies in the third year. What is the net gain to his family?
Ans. $ 10657.20.