Note.-Interest should be computed for the three days grace in each of the following examples.

14. What is the bank discount on a note for $465, payable in 6 months, at 6 per cent. ?

15 What is the bank discount on a note for $972, payable in 4 months, at 5 per cent.?

16. What is the bank discount on a note for $1492, payable in 3 months, at 7 per cent.?

17. What is the bank discount on a draft of $628, payable at 60 days sight, at 5 per cent.?

18. What is the present worth of $2135, payable in 8 months, at 7 per cent.?

19. What is the present worth of a note for $2790, payable in 1 month, discounted at 6 per cent. at a bank?

20. What is the bank discount, at 5 per cent., on a draft of $1747, payable at 90 days sight?

21. What is the bank discount, at 4 per cent., on a draft of $3143, payable in 4 months?

22. What is the bank discount on $5126.63, payable in 30 days, at 8 per cent.?

23. What is the bank discount on $3841.27, payable in 60 days, at 6 per cent.?

24. What is the present worth of a note for $6721, payable in 10 months, discounted at 6 per cent. at a bank?

25. What is the present worth of a note for $1500, payable in 12 days, at 7 per cent. discount ?

26. What is the bank discount on $10000, payable in 45 days, at 6 per cent.?

27. What is the bank discount on $25260, payable in 90 days, at 7 per cent.?

28. What is the difference between the true discount and bank discount on $5000 for 10 years, at 6 per cent.?

CASE II.

29. A man wishes to make a note payable in 1 year, at 6 per cent., the present worth of which, if discounted at a bank, shall be just $200 for what sum must the note be made?

Analysis. The present worth of $1, payable in 1 year, at 6 per cent. discount, is 100 cts.—6 cts.=94 cts.; that is, the present worth is of the principal or sum discounted. The question then resolves itself into this: $200 (present worth) is of what sum? Now, if $200 is of a certain sum,

is

of $200; and $200-94-$2.12766, and 188=$2.12766×100, which is $212.766. Ans:

Or, we may reason thus: Since 94 cents present worth requires $1, (100 cents) principal, or sum to be discounted for the given time, $200 present worth will require as many dollars, as 94 cents is contained times in $200; and $200÷$.94=$212.766.

PROOF

$212.766X.06=$12.7659, the bank discount for 1 year; and $212.766-$12.7659 $200, the given sum. Hence,

434. To find what sum, payable in a specified time, will produce a given amount, when discounted at a bank, at a given per cent.

Divide the given amount to be raised by the present worth of $1, for the time, at the given rate of bank discount, and the quotient will be the sum required to be discounted.

30. How large must I make a note payable in 6 months, to raise $400, when discounted at 7 per cent. bank discount?

31. What sum payable in 4 months must be discounted at a bank, at 5 per cent., to produce $950?

32. What sum payable in 60 days, will produce $1236, if discounted at a bank, at 8 per cent.?

33. For what sum must a note be drawn, payable in 34 days, the avails of which, at 6 per cent., bank discount, will be $2500 ?

34. For what sum must a note be drawn, payable in 90 days, so that the avails, at 7 per cent. bank discount, shall be $3745 ?

35. A man bought a farm for $4268 cash: how large a note, payable in 4 months, must he take to a bank to raise the money at 6 per cent. discount?

QUEST.-434. How find what sum, payable in a given time, will produce a given amount, at a given per cent., bank discount?

36. A man wishes to obtain $63240 from a bank at 6 per cent. discount how large must he make his note, payable in 1 month and 15 days?

37. What sum payable in 8 months, if discounted at a bank, at 6 per cent., will produce $10000 ?

38. What sum payable in 4 months, will produce $50000, if discounted at 7 per cent. at a bank?

39. A man received $46250 as the avails of a note, payable in 60 days, discounted at a bank at 5 per cent.: what was the face of the note?

40. A merchant wished to pay a debt of $8246 at a bank, by getting a note payable in 30 days discounted, at 8 per cent.: how large must he make the note?

INSURANCE.

435. INSURANCE is security against loss or damage of property by fire, storms at sea, and other casualties. This security is usually effected by contract with Insurance Companies, who, for a stipulated sum, agree to restore to the owners the amount insured on their houses, ships, and other property, if destroyed or injured during the specified time of insurance.

OBS. 1. Insurance on ships and other property at sea is sometimes effected by contract with individuals. It is then called out-door insurance.

2. The insurers, whether an incorporated company or individuals, are often termed Underwriters.

436. The written instrument or contract is called the Policy. The sum paid for insurance is called the Premium.

The premium paid is a certain per cent. on the amount of property insured for 1 year, or during a voyage at sea, or other specified time of risk.

OBS. 1. Rates of insurance on dwelling-houses and furniture, stores and goods, shops, manufactories, &c., vary from 3 to 2 per cent. per annum on the sum insured, according to the exposure of the property and the difficulty of moving the goods in case of casualty. It is a rule with most Insurance

QUEST.-435. What is Insurance? Obs. When insurance is effected with individuals, what is it called? What are the insurers sometimes called? 436. What is meant by the policy? The premium?

Companies not to insure more than two thirds of the value of a building, or goods on land.

2. Coasting vessels are commonly insured by the season or year. In time of peace, the rate varies from 4 to 7 per cent. per annum; in time of war it is much higher. Whale ships are generally insured for the voyage, at a rate varying from 5 to 8 per cent. on the sum insured.

3. When the general average of loss is less than 5 per cent., the underwriters are not liable for its payment.

CASE I.

437. To compute Insurance for 1 year, or a specified time. Multiply the sum insured by the given rate per cent., as in interest. (Art. 404.)

Ex. 1. A man effected an insurance on his house for $500, at 11 per cent. per annum: how much premium did he pay?

Solution.-$1500×.0125 (the rate)=$18.75. Ans.

2. What is the premium for insuring a store to the amount of $2760, at 3 per cent.?

3. What premium must I pay for insuring a quantity of goods, worth $6280, from New York to Liverpool, at 1 per cent.?

4. What is the annual premium for insuring a stock of goods, worth $10200, at per cent.?

5. What is the annual premium for insuring a coasting vessel, worth $1600, at 6 per cent.?

6. A bookseller shipped a quantity of books, valued at $4700, from Boston to New Orleans, at 1 per cent. insurance: what amount of premium did he pay?

7. A merchant shipped a cargo of flour, worth $45000, from New York to Liverpool, at 2 per cent.: how much premium did he pay?

8. What is the insurance on a cargo of teas, worth $75000, from Canton to Philadelphia, at 2 per cent.?

9. What is the annual insurance on a factory, worth $65000, at per cent.?

10. A powder mill was insured for $1945, at 12 per cent.: what was the annual premium?

QUEST.-437. How is insurance computed for 1 year or a specified time?

11. A ship embarking on an exploring expedition, was insured for $45360, at 8 per cent. per annum: what did the insurance amount to in 5 years?

12. A policy of insurance for $45000 was obtained on a whale ship, at 7 per cent. for the voyage: what was the amount paid for insurance?

CASE II.

13. If a man pays $16 annually for insuring $800 on his shop, what per cent. does he pay?

Analysis.—If $800, the amount insured, costs $16 premium, $1 will cost of $16; and $16÷800=.02; which is 2 per cent. PROOF.-$800X.02-$16, the premium paid. Hence,

438. To find the rate per cent. when the sum insured and the annual premium are given.

Divide the given premium by the sum insured, and the quotient. will be the rate per cent. required.

Note. This case is similar in principle to Problem II. in Interest.

14. If a man pays $60 annually for insuring $2400 on his house, what per cent. does it cost him?

15. A merchant pays $200 per annum for insuring $8000 on his goods: what per cent. does he pay?

16. A grocer paid $122.50 premium on a cargo of flour, worth $12250, from Charleston to Portland: what per cent. did he pay?

17. An importer paid $350 insurance on a quantity of cloths, worth $28000, from Havre to New York: what per cent. did he pay?

CASE III.

18. A man pays $45 annually for insuring his library, which is per cent. on the amount of his policy: what is the sum insured? Analysis. Since 3 cents will insure $1 at the given rate, for a year, $45 will insure as many dollars as 3 cents are contained times in $45; and $45÷.03=$1500. Ans.

PROOF. $1500X.03 $45, the given premium. Hence,