3. How much stock at 1004 will £1600 purchasë?

4. How much stock in the 3 per cent. reduced annuities may be bought for £1290, when the price is at 801 ?

CASE III. To find the rate of interest arising from money in the stocks.

RULE. As the price of any kind of stock, is to £100, so is the dividend on £100 of that kind of stock to the rate of interest arising from money vested in it.

EXAMPLE.

What rate of interest arises from money vested in the 3 per cent. cons, when the price is at 671⁄2?

67: 100 :: 3 £4 8 8 per cent.

EXERCISES.

1. What rate of interest arises from money in the 4 per cent. cons., when the price is at 95 ?

2. What rate of interest arises from money vested in the 3 per cent. cons., when the price is at 57?

3. What rate of interest arises from money vested in India stock, when the price is at 240; the dividend being 10 per cent. ? 4. At what rate must the 3 per cents. and the 4 per cents. sell respectively to yield 5 per cent. on money vested in them? 5. How much money must be laid out in the 3 per cent. cons. at 793 to produce an income of £100 a-year?

6 How much a-year in the long annuities can I purchase for £4005, when the price is 18 years purchase, allowing per cent. on the cost for brokerage?

INSURANCE.

Insurance is a contract by which one party engages, for a stipu lated sum, to exempt another party from a risk to which he is exposed.

The persons who take upon them the risk, are called the insurers, or underwriters; and the persons exempted from the risk, are called the insured. The sum paid to the insurers, is called the premium; and the paper or parchment containing the contract, is called the policy.

CASE I. To find the premium.

RULE. Calculate as in Commission; and when the rate is expressed in guineas, calculate as if it were pounds, and then add a twentieth part to the answer.

5

Note. The duty on policies of insurance against loss by fire is 3/ per £100 insured; the duty on sea insurances is 2/6 per £100, for voyages from one part of the. United Kingdom to another, and 5/pet £100, for any other voyage. Policy duty is reckoned on the fractional parts of £100, as if they amounted to £100: thus, the duty on £520 or £580 is the same as the duty on £600.

EXAMPLE.

Find the expense of insuring £850 on a cargo of flax from Rotterdam to Dundee, at 2 guineas per cent., policy duty 5/, and commission per cent.

5/1419,00

£2 5

1 1 3

£22 6 3

2,00)8,50

£4 5 0

Premium on £850 at 24 gs. per cent. £22 6 3

2 5 0
45.0

£28 16 3

Remark. In time of war, insurances are often effected at a high premium, with a stipulation to return so much per cent., if the ship sail with convoy, and

arrive.

EXERCISES.

1. Find the expense of insuring £580 from Greenock to Dublin, at 14 guineas per cent., policy 2/6 per cent., and commission per cent.

.

2. Find the expense of insuring £1745 on a cargo from Leith to Riga, at 34 guineas per cent., policy 5/ per cent., and com. mission per cent.

3. Find the expense of insuring £984: 10 on goods from Kingston to Bristol, at 6 guineas per cent., policy 5/ per cent., and commission per cent.

4. Find the yearly expense of insuring £2000 on a house, from damage by fire, premium 2/ per cent., and policy 3/ per cent. 5. Find the expense of insuring £212: 15 on goods from Leith to

Orkney, at 1 per cent., policy 2/6 per cent., and commission per cent.

6. Find the expense of insuring £790 on a ship from Gottenburg to Aberdeen, premium 5 guineas per cent., to return 2 per cent. for convoy and arrival, policy 5/ per cent, commission

per cent.; the vessel having sailed with convoy, and arrived at her port.

7. Find the expense of insuring £5000 on a cargo from Port Ma. ria to Hull, at 8 guineas per cent., to return 3 per cent., if the ship sail with convoy and arrive, which took place, policy 5/, and commission per cent.

CASE II. To find how much must be insured to cover a given sum. RULE. Subtract the sum of the premium, policy, and commission per cent. from £100: then, as the remainder is to £100, so is the given sum to the sum to be insured.

EXAMPLE.

How much must be insured to cover £1880, premium 5 guineas, policy 5/, and commission per cent ?

Premium

£5 5 0

Policy and comm. 0 15 0

£100-6 0 0 £94: £100:: £1880: £2000. Ans. Remark. To cover property is to insure not only the value of the property, but also the premium and other expenses, so that the owner may be fully in demnified in case of a total loss. Thus, if the owner of the goods in the above example insure £2000, and if a total loss happen, he will recover £2000 from the insurers; from which, if the amount of the premium, which is £105, of the policy, which is £5, and of the commission, which is £10, be deducted, the net sum saved is £1880, so that he is fully indemnified for the loss.

EXERCISES.

1. How much must be insured to cover £500, premium 24 guineas, policy 2/6, and commission per cent.?

2. How much must be insured to cover £875, premium 4 guineas, policy 5/, and commission per cent. ?

3. How much must be insured to cover £1500, premium 3 guineas, policy 5/, and commission per cent. ?

CASE III. To compute averages.

RULE. As the whole value of any article is to the whole loss, so is each man's share of that article to his proportional average of the loss; or so is £100 to the average loss per cent.

EXAMPLE.

A ship on a voyage to London, having been overtaken by a a storm, sustained the following losses: masts, cables, and rigging cut away, the expense of replacing which was £450; an anchor lost, which cost £50; 5 puncheons of rum thrown overboard, value £100; and charges of pilotage, &c. £50. The value of the ship was £4000; the net proceeds of the cargo, per account-sales, £7000; the gross freight £1590, from which deduct portage bill £90. Only £2000 were insured on account of the ship, and £4500 on the cargo. Find the general average loss per cent., and how much of it each party must pay.

Cost of replacing masts, cables, and rigging
Deduct for newness .

£450

150

-£300

50 100

50

£500

Underwriters pay for ship 4 per cent. on £2000

£80

Remarks. Average is a contribution made for losses at sea. Averages are dis tinguished into general and particular.

General average is a proportionable contribution made by all the proprietors of a ship, cargo, and freight, for losses incurred with a view to safety; such as throwing goods overboard to lighten the vessel; cutting away masts to prevent shipwreck; and the like. Sacrifices of this kind, however, must be made in consequence of a deliberate consultation held between the master and sailors. The loss must be the effect of a voluntary action, and the object of that action, the common safety of the whole.

Particular average is a partial loss of the ship or cargo occasioned by the. common accidents of the sea; and must be borne by the owners of the article that suffers damage.

2. In computing a general average for masts, cables, rigging, &c. cut away, a deduction is made of one-third from the cost of replacing them, as the new articles are supposed to be so much better than the old. But goods thrown overboard are valued at the sum they would have brought had they arrived safe.. 3. Underwriters are liable for general and particular averages, in proportion to the sums which they have underwritten. Thus, if a person underwrite £100. upon a property valued at £500, and if a total loss happen, he is answerable only for £100; if a partial loss happen, amounting to £60 per cent. on the whole value, he must pay £60, being his proportion of the loss.

4. When goods are damaged, the underwriters must pay the owners such proportion of the prime cost, or value mentioned in the policy, as corresponds with the proportion of the diminution in value occasioned by the damage. Thus, if the value in the policy be £30, and if the goods, though damaged, sell for £40, when, if sound, they would have sold for £50, the difference in value between the sound and damaged is one-fifth: consequently the underwriters must pay one-fifth of £30, or £6. On the contrary, had they come to a losing market, and sold, when damaged, for £10, when, if sound, they would have brought £20, the difference is one-half, and the underwriters must pay one-half of £30, or £15. When no valuation is stated in the policy, the invoice of the cost, with the addition of all charges, and the expense of insurance, is the foundation on which the loss is computed.

5. Ransoms are prohibited by law, and no sum paid on such account can be recovered from the underwriters.

6. The expense of Salvage, (which is fixed at one-eighth of the real value, if the recapture is made by any of his Majesty's ships, but one-sixth of the value, if by any other ship,) is paid by the underwriters.

7. In partial averages, the return of premium for convoy, is not allowed on the sum claimed for average.

8. General averages are always paid, how small soever they may be; but to prevent the underwriters from being harassed with trifling demands for particular averages, it is generally stipulated, that in insurances on corn, fish, salt, fruit, flour, and seed, the underwriters will not pay any particular average, unfess the ship be stranded: that, in insurances on sugar, tobacco, hemp, flax, hides, and skins, they consider themselves free from an average under 5 per

cent.; and that, on all other goods, as well as on the ship and freight, they consider themselves free from particular average under 3 per cent., unless the ship be stranded.

EXERCISES.

1. The ship Mary, on a voyage from Leith to Gottenburg, fell in with a Danish privateer, which, after a smart engagement, she had the good fortune to beat off. In the engagement, however, she sustained considerable damage; the expense of repairing which amounted to £120. The ship, which was valued at £800, and the freight, which amounted to £150, were insured at Leith. Of £1050, the value of the cargo, £500 were insured at Dundee, and the rest risked. Find the general average loss per cent., and how much of it each party had to sustain.

2. Insurance was made on 80 hhds. clayed sugars, on board the Vrow Martha, from the island of St. Thomas to Hamburgh, valued in the policy at £30 per hhd. In the course of the voyage, the sea water got in, and when the ship arrived at Hamburgh, it appeared that every hlid. of the sugar was damaged. The damage the sugars had sustained, made it necessary to sell them immediately, and they were accordingly sold for £20:0: 8 per hhd.; whereas had they been sound, they would at that time have brought at Hamburgh £23: 7:7 per hhd.: how much per cent, and in all, did the proprietor of the sugar recover from the underwriters ?

3. The ship Frances, on a voyage from Antigua to London, suffered the following losses: masts, cables, and rigging cut away, the expense of replacing which was £300; an anchor lost, which cost £45; 9 puncheons of rum thrown overboard, value £180; pilotage and other expenses in bringing the ship to port, £34:3: 4. Of 100 hhds. of sugar, valued in the poli cy at £25 per hhd., part was so much damaged, that the deficiency of 35 hhds., on a comparison with the 65 hhds. that arrived free from damage, was 18 hhds. The ship was valued at £2500; the net proceeds of the cargo per account sales were £4000; the gross freight, £900; portage bill £150. The ship, cargo, and net freight were insured at 12 guineas per cent., to return 6 per cent. for convoy and arrival, which took place. How much per cent. had the underwriters to pay for general and particular averages, and how much in all to the proprietor of the sugar, including the return of premium ?

LOSS AND GAIN.

CASE I. When the prime cost, and the gain or loss on it are given, to find the gain or loss per cent.