are to receive one-fourth per cent on the money they advance: how much must A pay them for the stock? Ans. $39498,50. 6. Messrs. P, W and K receive $28750 to be invested in stock. They charge 2 per cent commission on the amount paid: what is the value of the stock purchased? Ans. $28048,78+.

7. The par value or first cost of 167 shares of bank stock was $200 per share: what is the present value, if the stock is at a premium of 25 per cent, that is, 25 per cent above par. Ans. $ 8. What would be the value of the stock named in the last example, if it were at a discount of 10 per cent?

Ans. $30060. 9. One hundred shares of United States Bank stock is worth 18 per cent premium: the par value being $200 per share, what is the value of the stock? Ans. $23700.

10. A bank fails, and has in circulation bills to the amount of $267581. It can pay 9 per cent: how much money is there on hand?

Ans.

11. Sixty-nine shares of bank stock, of which the par value is $125, is at a discount of 8 per cent: what is its value? Ans. $7935.

Q. What is commission? What is brokerage? How is the allowance generally made? How is the commission or brokerage found? How do you find the amount of stock to be purchased when the broker receives a certain per cent on the amount purchased, as in example 3?

INSURANCE.

§ 163. Insurance is an agreement by which an individual or a company agrees to exempt the owners of certain property from loss or hazard.

The written agreement is called the policy.

The premium is the amount paid by him who owns the property, to those who insure it, as a compensation for their risk. It is generally so much per cent on the value of the property insured.

EXAMPLES.

1. What would be the premium for the insurance of a house valued at $5500 against loss by fire for 1 year at per cent.

1

By dividing by 100, we have the insurance at per cent.

The half, is the insurance at half per cent.

{ 55,00

$27,50.

2. What would be the premium for insuring a ship and cargo, valued at $37500 from New York to Liverpool, at 31 per cent?

Ans. $

3. What would be the insurance on a ship valued at $47520 at per cent: also at per cent? Ans. $237,60.-$158,40. 4. What would be the insurance on a house valued at $14000 at 1 per cent? Also, at per cent? At per cent? At per cent? At per cent?

Ans. $210.-$105.—$70.—$46,66+.—$35.

5. What is the insurance on a store and goods, valued at $27000, at 21 per cent? At 2 per cent? At 1 per cent? At per cent? At per cent? At per cent? At per cent? At per cent?

Q. What is insurance? What is the policy? What is the premium? How is it generally reckoned?

DISCOUNT.

§ 164. If I give my note to Mr. Wilson for $106, payable in one year, the present value of the note will be less than $106 by the interest on its present value for one year: that is, its present value will be $100.

The amount named in a note is called the face of the note. Thus $106 is the face of the note to Mr. Wilson. The present value of a note is that sum which being put at interest until the note becomes due would increase to an amount equal to the face of the note. Thus $100 is the present value of the note to Mr. Wilson.

The discount is the difference between the face of a note and its present value. Thus, $6 is the discount on the note to Mr. Wilson.

RULE.

As 100+ interest of $100 for the given time, is to 100, so is the face of the note to its present value.

EXAMPLES.

1. What is the present value of a note for $1828,75 due in one year, at 4 per cent per annum?

2. What is the present value of a note for $1290,81 discounted for four months, at 6

per cent per annum? Ans. $1265,50. 3. What is the present value of $800, due 4 years hence the interest being computed at 5 per cent per annum? Ans. $666,66 6+.

NOTE. When payments are to be made at different times, find the present value of the several sums separately and their sum will be the present value of the note.

1. What is the present value of a note for $3500 on which $300 are to be paid in 6 months; $900 in one year; $1300 in eighteen months; and the residue at the expiration of two years: the rate of interest being 6 per cent per annum? Ans. $3225,83+. 5. What is the discount of £1500 one-half payable in 6 months and the other half at the expiration of a year, at 7 per cent per annum? Ans. £ +. 6. What is the present value of $2880, one-half payable in 3 months, one-third in 6 months, and the rest in 9 months at 6 per cent per annum? Ans. $2810,08+.

Q. What is the face of a note? What is the present value of a note? What is the discount of a note? How do you find the present value of a note? When payments are to be made at different times, how do you find the present value?

LOSS AND GAIN.

§ 165. Loss and Gain is a rule by which merchants discover the amount lost or gained in the purchase and sale of goods. It also instructs them how much to increase or diminish the price of their goods so as to make or lose so much per cent.

EXAMPLES.

1. Bought a piece of cloth containing 75yd. at $5,25 per yard, and sold it at $5,75 per yard: how much was gained in the trade?

2. Bought a piece of calico containing 50yd. at 2s 6d per yard: what must it be sold for per yard to gain £1 Os 10d?

3. Bought a hogshead of brandy at $1,25 per gallon, and sold it for $78: was there a loss or gain?

Ans. loss of $0,75. 4. A merchant purchased 3275 bushels of wheat for which he paid $3517,10, but finding it damaged is willing to lose 10 per cent: what must he sell it for per bushel? Ans. $0,96+.

5. A bought a piece of cotton containing 40 yards, at 6 cents per yard; he sold it for 7 cents per yard: how much did he gain? Ans. $0,60.

6. Bought a piece of cloth containing 75 yards for $375: what must it be sold for per yard, in order to gain $100? Ans. $6,33 per yard.

7. Bought a quantity of wine at $1,25 per gallon, but it proves to be bad and am obliged to sell it at 20 per cent less than I gave: how much must I sell it for per gallon? Ans. $1 per gall.

8. A farmer sells 125 bushels of corn for 75cts. per bushel; the purchaser sells it at an advance of 20 per cent: how much did he receive for the corn? Ans. $

9. A merchant buys one tun of wine for which he pays $725, and wishes to sell it by the hogshead at an advance of 15 per cent: what must he charge per hogshead?

Ans. $208,43+.

10. A merchant buys 158 yards of calico for which he pays 20 cents per yard; one-half is so damaged that he is obliged to sell it at a loss of 6 per cent; the remainder he sells at an advance of 19 per cent: how much did he gain? Ans. $2,05+.

EQUATION OF PAYMENTS.

§ 166. I owe Mr. Wilson $2 to be paid in 6 months; $3 to be paid in 8 months; and $1 to be paid in 12 months. I wish to pay his entire dues at a single payment, to be made at such a time, that neither he nor I shall lose interest at what time must the payment be made?

The method of finding the mean time of payment of several sums due at different times, is called Equation of payments.

Taking the example above. Int of $2 for 6mo. " of $3 for 8mo. " of $1 for 12mo.

int. of $1 for 12mo. 2x 6=12 int. of $1 for 24mo. 3x 8=24 int. of $1 for 12mo. 1x 12=12

9$

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