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repairs of the school-house $30, and for teacher's salary $ 150, and the public money amounts to $ 50. If the rate bills require to be made out at the rate of 3 cents a day for each pupil's attendance, what was the aggregate attendance ?

Ans. 5000 days. 5. J. Kimball had goods to the value of $ 7000 on board a vessel, which, from stress of weather, required cargo to the amount of $ 4000 to be thrown overboard, and of which the value of $ 3000 belonged to Kimball. If, in adjusting the general average, the several contributory interests pay 5 per cent., to what sum will Kimball's loss be reduced ?

Ans. $ 350. 6. A owes B $ 150, $ 50 to be paid in 4 months, and $ 100 in 8 months. B owes A $ 250 to be paid in 10 months. It is agreed between them that A shall make present payment of his whole debt, and that B shall pay his so much sooner as to balance the favor. Required the time at which В must pay the $ 250.

Ans. 6 months. 7. A debt is to be paid down, 1 in 6 months, & in 8 months, and the balance in 12 months. If the payments were all converted into one, on what credit should it be? Ans. 5mo. 25d.

8. A merchant proposes to admit a young man into business with him, on condition that, if he put into the stock $ 2000, his pay shall be $ 800 a year, or if he put in $ 4000, he shall have $ 1100 a year; in this offer what was allowed for his services

Ans. $ 500. 9. A gentleman is owing three notes to George Shannon, one of $ 100 dne in 4 months, another of $ 100 due in 8 months, and a third of $ 200 due in 12 months. Should the three notes be converted into two for the same amount, the one to run just twice as long as the other, when ought they to be made payable ? Ans. The one in 6mo., and the other in 12mo.

10. An account settled January 1, 1858, showed a balance of debts to the amount of $ 360, and a balance of interest in favor of the credit side to the amount of $ 3.78; how long in equity ought the balance of debts to remain unpaid after the day of settlement, exactly to offset this balance of interest, allowing the rate of interest to be 6 per cent. ? Ans. 63 days.

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INSURANCE.

442. INSURANCE is a contract of indemnity, by which one party engages, for a stipulated sum, to insure another against a risk or loss to which he is exposed.

The insurer or underwriter is the party taking the risk.

The premium is the sum paid for insurance, and is generally reckoned at a certain per cent. of the value of the property insured.

The policy is the written obligation or contract. NOTE. — Insurance is generally made by an incorporated joint-stock company, and sometimes by individuals. When each person insured becomes a member and proprietor in the profit or loss of the concern, it is called a mutual insurance company. Many companies, as a security against fraud, do not insure property for its full value.

FIRE AND MARINE INSURANCE.

443. Fire Insurance is that which indemnifies damage and loss caused by fire or lightning.

444. Marine Insurance is that which indemnifies damage and loss caused by the perils peculiar to navigation.

445. To compute the premium of insurance on any given amount at a specified rate.

Ex. 1. What would be the premium for insuring a house, valued at $ 5728, at 1} per cent. ?

Ans. $ 100.24.

OPERATION.

$5728 x .013= $ 100.24. RULE. Find the percentage of the given sum at the rate of insurance, and the result is the premium.

NOTE. When the amount insured and the premium are known, the rate of insurunce may be found by Art. 350.

EXAMPLES.

2. What is the premium for insuring a house valued at $ 896, at 12 per cent. ?

Ans. $ 107.52. 3. How much would be required to be paid to effect the insurance of a brig valued at $ 17,289, at 14 per cent. ?

Ans. $ 216.114

4. My ship Keystone State is valued at $ 35000, and her cargo at $ 75000. I procure an insurance on of the value of the ship, at 31 per cent., and on şof her cargo, at 24 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. $180.153.

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 41 per cent.; the second year, 33 per cent.; the third year, 43 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. 446. 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. ?

OPERATION.

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$ 2475 ; .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. - Divile the value of the property to be covered by 1 de. creased 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.

EXAMPLES

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 124 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 11 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.

LIFE INSURANCE.

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

TABLE.

1

0 38.72 28.15 1 | 44 68 36.78 2 47.55 38.74

49.82 40.01 4 50.76 40.73 5 51.25 40.88 6 51.17 40.69 7 50.80 40.47 8 50.24 40.14 9 49.57 39.72 10 48.82 39.23 11 48.04 38.64 12 47.27 38.02 13 46.51 37.41 14 45.75 36.79 15 45.00 36.17 16 44.27 35.76 17 43.57 35.37 18 42 87 34.98 19 42.17 34.59 20

41.46 34.22 21 40.75 33.84 22 , 40.04 33.46 | 23 39.31 33.08

24 38.59 32.70
25 37.86 32.33
26 37.14 31.93
27 36.41 31.50
28 35.69 31.08
29 35.00 30.66
30 34.34 30.25
31 33.68 29.83
32 33.03 29.43
33 32.36 29.02
34 31.68 28.62
35 31.00 28.22
36 30.32 27.78
37 29.64 27.34
38 28.96 26.91
39 28.28 26.47
40 27.61 26.04
41 26.97 25.61
42 26.34 25.19
43 25.71 24.77
44 25 09 24.35
45 24.46 23.92
46 23.82 23.37
47 23.17 22.83

48 22.80 22.27
49 21.81 21.72
50 21.11 21.17
51 20.39 20.61
52 19.68 20.05
53 18.97 19.49
54 | 18 28 18.92
55 17.58 18.35
56 16.89 17.78
57 16.21 17.20
58 15.55 16.63
59 14.92 16.04
60 14.34 15.45
61 13.82 14.86
62 13.31 14.26
63 12.81 13.66

12.30 13.05
65 11.79 12.43
66 11.27 11.96

10.75 11.48
68 10.23 11.01
69 9.70 10.50
70 9.18 10.06
71
8.65

9.60

72 8.16
73 7.72
74 7.33
75 7.01
76

6 69
77 6.40
78 6.12
79 5.80
80 5.51
81 5.21
82 4.93
83 4.65
84 4.39
85 4.12
863.90
87 | 3.71
88 3.59
89 3.47
90 3.28
91 3.26
92 3.37
93 3.48
94 3.53
95 3.53

9.14 8.69 8.25 7.83 7.40 6.99 6.59 6.21 5.85 5.50 5.16 4.87 4.66 4.57 4.21 3.90 3.67 3.56 3.73 3.32 3.12 2.40 1.98 1.62

64

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 Boston, and by the Girard Life Insurance Annuity and Trust Company, of Philadelphia, are given in the following

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