CASE IV. 581. To find the return premium on a cancelled policy. 582. To Cancel a Policy is to annul the agreement between the party insured and the insurers. 1. When the policy is canceled at the instance of the company, a pro rata proportion of the premium paid is returned; when done at the request of the policy holder, the company pay back a return premium governed by what are known as Short Rate Tables. 2. When a partial loss has been paid, the return premium is to the whole premium as the balance of the policy after deducting the partial losses paid is to the whole amount of the policy as first issued. 1. Mr. A effects an insurance on his stock of mdse. to the amount of $5000 for 6 mo., at short rates, his risk being rated at 85 on a hundred dollars; in consequence of a reduction of stock at the end of 4 mo., he wishes his policy cancelled; to how much return premium is he entitled ? SOLUTION.-The rate for 6 mo. as found in the table is $.0059, and for 4 mo., $.0042; hence the return premium is the difference between $.0059 and $.0042 multiplied by 5000, or $8.50. OPERATION. .0059-0042-.0017 $.0017X 5000-$8.50 Rule.-Multiply the amount insured by the difference of the rates for the two periods, to find the return premium. WRITTEN EXERCISES. 2. Mr. B takes out a perpetual insurance on his marble dwelling to the amount of $5500, his risk being rated at % annually; what is the deposit premium at the rate of ten annual premiums, and if he afterward surrenders his policy for cancellation, how much return premium should he get the rate being 90% of the deposit ? Ans. $137.50; $123.75. 3. Mr. C has an annual policy of insurance of $2500 on his house; at the end of 7 mo. a fire occurs which damages his property to the amount of $500, which the insurance company pays and indorses the payment on his policy; 2 mo. afterward Mr. C sells his house and surrenders his policy for cancellation ir full; what is his return premium, the annual rate being % on his risk? Ans. $0.80. NOTE.-By the Table, the return premium for 9 mo. is .0026; hence (.003— 0028)X$2000 $.80. CASE V. 583. To adjust the loss on a risk between several different insurance companies. 584. When several companies are interested in a risk, a loss is sured by the companies in proportion to the amounts of the several policies. Companies usually attach on different items in the same propor tion. 1. W. & Bro. hold a policy of insurance on their mill for $5000 in the Delaware Mutual Fire Ins. Co., and also one for $4500 in the Fire Association; a fire causes a loss on the property to the amount of $1875; what amount does each of the companies pay? SOLUTION.-The whole amount insured is $9500; the amount of the loss to be paid by the Del. Mutual is to $1875 as $5000 is to $9500, which we find by proportion gives $986.84: the amount to be paid by the Fire Asso. is to $1875 as $4500 is to $9500, which gives $888.1515. OPERATION. 9500 1875X5000 -$986.84. x:$1875::4500:9500 x=$888.1515 Rule.-Divide the loss between the several companies in proportion to the amounts of the several policies. WRITTEN EXERCISES. 2. The Ins. Co. of North America issued a policy to Green & Co., covering $800 on their hotel building and $1700 on their furniture therein; the Sun Fire Ins. Co. also issued a policy to same parties, covering $2500 on the hotel, but nothing on the furniture. By a fire the building is damaged to the amount of $2200 and the furniture is damaged to the amount of $500; what proportion of the total damage does each company bear? Ans. N. Am., $1033.33; Sun, $1666.66. SUGGESTION.-The whole insured is $3300; N. Am.'s loss on the hotel is of $2200; Sun's loss on the hotel is of $2200, etc. NOTE.-Some practical problems involving greater complications, such as occur in business, may be found on page 392. Life Insurance, which is more difficult than Property Insurance, is presented on pages 393–5, PARTNERSHIP. 585. Partnership is the association of two or more persons for the transaction of business. 586. Partners are the persons associated in business, and are of three kinds, General, Limited, and Special. 587. The Capital of a firm is the money or property invested by the partners. The Liabilities are its debts. 588. The Resources or Assets of a firm are its property of any kind, together with the amounts due it. The excess of resources over liabilities is called the Net Capital. 589. Partnership is divided into Simple and Compound Partnership for convenience of treatment. General Partners risk their whole property in the business; Limited and Special Partners risk only the amount of capital they agree to contribute. Partners whose names do not appear are sometimes called Silent Partners. SIMPLE PARTNERSHIP. 590. In Simple Partnership the shares of the partners are employed for equal periods of time. 1. A, B, and C, went into partnership; A put in $500, B put in $700, and C, $800; they gained $600; what was each one's share of the gain? Rule.-Divide the gain or loss among the partners in proportion to their shares of the stock. WRITTEN EXERCISES. 2. A, B, and C form a partnership for shipping peaches; A puts in $680, B $720, C $600; they gain $600; what does each receive? Ans. A, $204; B, $216; C, $180. 3. Three persons enter into partnership, with $6000, of which A contributes 1, B, and C the remainder; they gain $1800 what sum belongs to each ? Ans. A, $900; B, $600; C, $300. 4. Three men agree to share 60 gal. wine, A taking, B , and C ; but upon drawing off these parts they find there is a remainder; how should the wine be divided? Ans. A, 2525 gal.; B, 19, gal.; C, 1515 gal. 5. A, B, and C were partners in the coal trade; A furnished $5000, B $7000, and C managed the business; they gained $2400; what was the share of each, if C received as much as both A and B? Ans. A's, $500; B's, $700; C's, $1200. 6. Three persons engage in cotton speculation; A contributed $6400, B $7200, and C $5400; they lose of their stock by fire, and gained on the remainder of cost; what was the gain of each ? Ans. A's, $2048; B's, $2304; C's, $1728. 7. 'Squire Jones left by his will $5000 to his wife, $350C to his son, and $4500 to his daughter; but upon settling his estate it was found to amount to only $10400; how much Idid each receive? Ans. Wife, $4000; son, $2800; daughter, $3600. SUPPLEMENTARY PROBLEMS. To be omitted unless otherwise directed. 8. A, B, and C go into the lumber trade with a joint capital of $9500; at the end of a year it is found that A's gain is $1650, B's $1500, and C's $1600; required each one's stock. Ans. A's, $3300; B's, $3000; C's, $3200. 9. A shipping firm gained one year $4200; A's stock was $6500, B's stock, $5300, and C's gain $1250; required C's stock and A's and B's gain. Ans. A's, $1625; B's, $1325; C's stock, $5000. 10. A, B, and C form a partnership for carrying on a nursery; A contributes $800, B $600, and C 10 acres of land on which to establish the nursery; their first year's profits are $1500, of which C receives $660; what are A's and B's gain, and the value of C's land per acre? Ans. A's, $480; B's, $360; $110 per acre. COMPOUND PARTNERSHIP 591. In Compound Partnership the capitals of the partners are employed for different periods of time. CASE I. 592. When the profits and losses are divided in proportion to capital and time. 1. Two persons enter into partnership and gain $328; A put in $800 for 5 mo., and B $700 for 6 mo.; what was each man's share of the gain? Rule. Multiply each partner's capital by the time it was employed, and divide the gain or loss in proportion to these products. 2. A, B, and C WRITTEN EXERCISES. engaged in partnership; A had $500 in trade for 9 mo., B $800 for 8 mo., and C $1200 for 7 mo.; they gain $488.70; what was each one's share of the gain? Ans. A's, $113.94; B's, $162.06; C's, $212.70 3. Four gentlemen rented a pasture-field for $62.40; the first put in 3 horses for 7 weeks, the second 4 horses for 8 weeks, the third 2 horses for 13 weeks, and the fourth 5 horses for 5 weeks; what should each pay? Ans. $12.60; $19.20; $15.60; $15. 4. A, B, C, and D agree to clear a tract of woodland for $120; A worked 9 days of 10 hours each, B 15 days of 6 hours each, O 10 days of 9 hours each, and D 3 weeks 5 hours a day; what does each receive? Ans. $30 5. Mr. Allen commenced business with $10000 capital; at |