4. George Holden, at 25 years of age, insures in the Mutual Life Insurance Company of New York, for $30,000, payable to himself in 20 years. If the dividends are added to the policy, and amount to $12,000, how much more will he receive than he has paid, reckoning 7% interest on premiums? Ans. He would pay $7634.88 more than he received. 5. At the age of 38 years, Joseph Moore took out a life policy of $5000, premiums to cease in 10 years. He died aged 44 years, 6 months; what was the gain by insuring, reckoning interest on premiums at 6% ? Ans. $2618.24. 6. Peter Lehr, 39 years of age, took out an endowment policy for $6000, payable in 10 years. In 15 months he died; what was the gain, reckoning interest on premium at 7%, and how much greater profit would it have been to take a life policy, premiums payable during life? Ans. $4653.89 gain; $964.81 more profit. 7. A clergyman insured for $2000 in 1843, in the Mutual Life Insurance Company of New York, and died in 1869, just after the payment of a premium, his heirs receiving as dividends, $1971.26. Supposing him to have been 45 years old at the issue of the policy, would it have been more profitable to have invested the premiums at 6% compound interest? Ans. They would have gained $866.555. CASE III. 929. Given, the age, the time, and the amount of the premiums, to find the amount of the policy. 1. A gentleman, 32 years old, took out an endowment policy for 15 years, and at its maturity he had paid in premiums $1813.32; what was the amount of his policy? SOLUTION. Since the premiums for 15 years amount to $1813.32, the premium for 1 year will be of $1813.32, which is $120.888. From the table we find that the annual premium on an endowment of $1000 at 32 years of age OPERATION. $1813.32-15= $120.888 $120.888 $67.16 = 1.8. $1000×1.8 $1800. for 15 years is $67.16; and since $67.16 is contained in $120.888, 1.8 times, the amount required must be 1.8 times $1000, or $1800. Rule. Find the annual premium and divide this by the premium in the table under the given age and rate, and multiply the quotient by $1000. NOTE. If interest is reckoned on premiums, divide the given amount by the amount of the premiums on $1000. 2. William Hoffman, of Lancaster, 25 years old, took out an endowment policy payable in 20 years, but died after making 12 payments, having paid as premiums $2288 64; what was the amount of his policy? Ans. $4000. 3. Joseph Duncan took out a life policy at the age of 51 years, and died just after making the 11th payment; his premiums, with interest at 6%, amounted to $10,596.30; what was the amount of his policy? Ans. $15,000. CASE IV. 930. Given, the amount of the policy, the premium, and the period of insurance, to find the age of the insured. 1. John Thompson insured his life for $3000, paying as premium $81.75; what was his age? SOLUTION. Since $3000 is 3 times $1000, we divide the premium $81.75 by 3, which gives $27.25, the premium on $1000. Looking in the table, we find $27.25 opposite 36 years, hence 36 years is the required age. OPERATION. $81.75-3=$27.25. Rule. Divide the annual premium by the ratio of the amount of the policy to $1000, and find the quotient in the table; the age opposite this number will be the age required. 2. Mrs. Mason took out an endowment policy for $2500, payable in 10 years; she paid $2817 as premiums until the policy matured; what was her age at the time of insuring? Ans. 50 years. 3. Edward Spencer took out a life policy for $8000, on the single payment plan; his premium was $3735.12; at what age did he insure? Ans. 42 years. 4. Lewis Levan took out an endowment policy for $5000 for 15 years, and at the time of maturity, his premiums, if put on interest at 6%, would have amounted to $7713.39; what was his age? Ans. 40 years. CASE V. 931. Given, the amount of the policy, the amount of the premiums, and the age, to find the period of insurance. 1. A gentleman, 43 years of age, was insured for life for $7000; the whole amount of premiums paid was $1717.45; at what age did he die? OPERATION. $35.05X7=$245.35 $1717.45 $245.35=7 7—1=6, 43+6=49 SOLUTION.-The premium on $1000, by the table, is $35.05, hence on $7000 it is $245.35; dividing $1717.45 by $245.35, we find the number of payments to have been 7; and since the first was made at the beginning of the period, there have been 6 yearly payments since he was 43 years old, hence his age was 43+6, or 49 years. Rule. Find the annual premium on the given sum, and divide the amount of the premiums by this annual premium; the result will be the period of insurance. 2. An endowment policy for $9000, was taken out by a lady aged 49 years; at its maturity she received $1062.90 less than she had paid in premiums; what was the period of the policy? Ans. 10 years. 3. John Wise, at the age of 30, insured his life for $5000, premium to be paid during 20 years; but dying before the expiration of the period, he paid in premiums $607.20 less than if he had made all the payments; how many payments did he make? Ans. 16. 4. Nathan Ward had his life insured at the age of 37, premiums payable during life; how long must be live that the amount of premiums paid may exceed the policy? Ans. Till his 73d year. 5. Peter Long takes out an endowment policy for $11,000, at the age of 42; at its maturity he has paid in premiums $11,635.80; what was the period of the policy? Ans. 20 years. NOTE. For formulas for obtaining the premium, etc., see Manual. 19* BUILDING ASSOCIATIONS. 932. Building Associations are coöperative corporations instituted to receive small deposits at regular periods, and to invest these in loans among the depositors or members, on mortgages given by the borrower. These associations enable many persons of moderate earnings and incomes to erect or buy buildings, and to invest their savings securely and profitably. The regular installments form the capital of the association, which is loaned to members only. The business is managed directly by the depositors, and the profits are equitably divided among them 933. The Members of an association are those who subscribe for shares. They are of two classes, borrowers, or those who borrow money of the association, and non-borrowers, who subscribe for shares as an investment. 934. The Shares are usually issued periodically in series, thus producing a constant succession of shares, each series successively reaching its value and being wound up, and a new series taking its place. Many associations have only one series. When the installments and profits on any series have raised the value of its shares to par, it is wound up by returning to the non-borrowing members the value of their shares (though in some associations the paid-up shares are allowed to remain and draw cash dividends), and to the borrowing members their mortgages and cancelled obligations. Thus, supposing $200 to be the value of a share and the payments $1 a month, if the capital is accumulated in one hundred months, the nonborrowing member will receive $200 on a share, and the borrowing member's debts will be cancelled, and his mortgage for $200 a share returned. The installments in each case have amounted to only $100, making a profit of $100, or 100% for the time. Many series are closed before their shares are fully equal to $200 in value. 935. The Dues are the fixed periodical installments, and are usually $1 a month. Contingent Dues for current expenses are assessed annually by some associations. In case of non-payment of dues, fines are levied. It is illegal in Pennsylvania to charge fines on unpaid fines. At the regular monthly meetings of associations, the aggregate installments or dues, interest, fines, etc., paid in, are loaned to the highest bidder, or sometimes in the order of application, in which latter case there is a fixed or stated premium to be paid by the borrower. 936. The Premium is a percentage paid per share, in excess of interest, on money which is "bought" or borrowed of the association. It is quoted for the beginning of the series. 937. The Stated Premium is the minimum rate fixed by associations, at which money will be sold on shares, each year of a series. The Stated Premium is fixed at $50, or 25% of a share, for the 1st year; $45, or 22% for the 2d year; $40, or 20% for 3d year, etc.; decreasing 10% yearly to the 7th year, when it becomes $20, or 10%. Money is seldom loaned after the 7th year, or at a lower "stated premium." The entire premium for any year of a series equals the stated premium for that year plus the amount bid. Some associations have no stated premium to regulate the difference of premium between different series, but deduct, for each expired year of the series, 10% from the premium bid. This is avoided by the Installment plan, in which a number of cents a month is bid as premium, thus making no difference in what series the borrower holds shares. 938. There are Three Modes of loaning money and fixing the interest, adopted by different associations, called the Installment Plan, the Net Plan, and the Gross Plan. By the first plan, the par value of a share is loaned on each share, and the premium is paid in monthly installments, together with the dues and interest. By the second plan, the premium is deducted from the par value, and interest is charged on the net amount of the loan. By the third plan, the premium is deducted from the par value, but interest is charged on the par value of the share. Thus, by the Installment Plan, the net loan is $200, the par value of the share and the full amount of the mortgage; the payments are $1 a month dues, $1 interest, and cents premium. By the Net Plan, if the premium is $50, the net loan is $150, and payments $1 a month dues and 759 a month interest. By the Gross Plan, the net loan is $150, but payments are $1 dues and $1 interest. The monthly premium in cents by the first plan corresponds nearly to the total premium in dollars on a new series by the other plans, on the basis of 100 months. In Pennsylvania, where these associations are most numerous, the number of shares at any one time is limited to 5000, and the periodic payments of borrowers to $2. Thus, by the Installment and Gross Plans, the dues and interest at 6% on $200, par value of a share, are each $1 a month, which brings the payments up to the limit, $2. If loans are paid before the termination of a series, an equitable part of the premium paid is refunded, by the Gross and Net Plans. No premium is returned by the Installment Plan, since none is paid in advance. The Installment and Net Plans are more favorable to the borrower than the Gross Plan. Of the three, the Installment Plan is the true one, and merits universal adoption. 939. A Withdrawal is made by returning the stock certificates to the association, and making settlement. |