eration for finding the sum to ensure, being omitted in this.

4. I have shipped goods to the value of $9165,60, how much must I ensure to cover both principal and premium, when I pay 5 per cent ? Ans. $9648. 5. What must be paid for ensuring $4630, at 7 per cent ? Ans. $347,25. 6. I shipped goods and ensured $6000, which covered principal and premium, and paid 5 per cent; what was the value of the goods? Ans. $5700.

NOTE. The value of the goods is found by finding the premium for $6000 at 5 per cent. and subtract the premium thus found, from the sum it was found for.

7. A merchant shipped goods to the amount of $4000, paid charges of shipping $60, freight he is to Pay $100, the duties at the foreign port he expects will be $50, he ensures the whole at 54 much does he pay for ensurance ?

per cent; how Ans. $231,25.

BROKERAGE.

Brokerage is the pay or reward of a broker, who procures a market for goods, &c. and is sometimes so much per cent, on the amount of the goods sold by their assistance; sometimes so many shillings per cent, or rather so many shillings on every 100 pounds, which is meant when expressed, so many shillings per cent; sometimes it is expressed so many cents per cent. which is understood so many cents on every 100 dollars, &c.

NOTE. Questions in this rule are proved by varying their order. See the second example varied for proof. CASE I. When the brokerage is so much per cent. as 1 per cent, 5 per cent, &c. proceed as in finding the commission.

EXAMPLES.

1. A broker has procured the sale of goods for me, to the amount of $2563,25; what will his brokerage come to at 1 per cent? Ans. $38,44,8, 75.

2. My broker has procured the sale of goods for me to the amount of $7369,46; what will his brokerage come to at per cent? Ans. $36,84,7,3.

To prove this.

3. If I pay a broker $36,84,7,3, and allowed him per cent. to what amount did he find sale for me?

CASE II. When the brokerage is so many shillings &c. per cent.

RULE. Divide the given sum by 100, and then take parts of the quotient with the rate per cent.

EXAMPLES.

1. What will the brokerage for £7364 11 6 come to at 4s. 6d. per cent ?

2. What is the brokerage for £700 14 6, at 4s. per

cent ?

3. What is the brokerage for £500

¿cent?

4. What is the brokerage for £909 per cent?

Ans. £1 8 04. 10 7, at 7s. per Ans. 1 15 04. 14 10, at 6s. 6d. Ans. £2 19 14.

CASE III. When the brokerage is so many cents

per cent.

In this case are four varieties.

Variety 1. When the given sum is dollars only.

RULE. Multiply the given sum by the cents per cent, and point off four places of right hand figures, those at the

P

left of the point will be dollars, the next two figures at the right of the point, are cents, the next figure a mill, or mills, &c.

EXAMPLES.

1. What is the brokerage for $7364, at 36 cents per cent?

7364
36

36)26,51,0,4(87364 proof.

252

2. What is the brokerage of $9643, at 75 cents per cent?

Ans. $72,32,2,5. 3. A broker has sold goods for me, to the amount of $17630; what must I pay him, allowing 80 cents per cent? Ans. $141,04.

Var. 2. When the given sum is dollars and cents. RULE. Multiply as in the first variety, and point off six right hand figures, all at the left of the point will be dollars, &c. as before.

EXAMPLES.

1. Required the brokerage for $9642,36, at 47 cents per cent. 9642,36

47

6749652

3856944

Ans. $55,31,9,092

2. A broker has procured the sale of goods for me, to the amount of $11637,75; what may he demand when I allow him 55 cents per cent ?

Ans. $64,00,7,625.

Var. 3. When the given sum is dollars, cents, and

mills.

RULE. Multiply by the cents as before, and point off seven places of right hand figures, those at the left of the point will be dollars, &c.

EXAMPLES.

1. What is the brokerage for $9375,23,7, at 73 cents per cent ? Ans. $68,43,9,2301. 2. Required the brokerage for $1637,27,9, at 48 cents per cent. Ans. 87,85,8,9392.

Var. 4. When the brokerage is cents and mills.

RULE. Multiply the given sum by the given cents and mills, and if the given sum be dollars, point off five right hand figures.

If dollars and cents, point off seven.

If dollars cents and mills, point off eight of the right hand figures, those at the left of the point will be dollars, the next two at the right of the point will be cents, the next one, a mill or mills.

EXAMPLES.

1. What is the brokerage for $9364, at 57 cents, 7 mills per cent?

9364

57,7

65548

65548

46820

Ans, dole. 54,03,0,28

2. What is the brokerage for dols. 7367,25, at 75 cents, 5 mills?

Ans. dols. 55,62,2,7375.

3. What is the brokerage for dols. 11963,21,7, at 48 cents, 5 mills per cent? Ans. dols. 58,02,1,60245.

EQUATION OF PAYMENTS,

When several sums of money to be paid at different times, are reduced to one mean time for the payment of the whole, without loss or gain to the debtor or creditor; this is called Equation of Payments.

To find the mean or equated time.

RULE. Multiply each payment by its time, add all the products together, and divide their sum by the whole debt; the quotient will be the equated time.

EXAMPLES.

1. A owes B 100 dols. whereof 50 dols. are to be paid at 2 months, and 50 dols. at 4 months; but they agreed to reduce them to one payment; when must the whole be paid?

50

50

50

2. A merchant has owing to him 300 dols. which is to be paid as follows, viz. 50 dols. at 2 months, 100 dols. at 5 months, and the remainder at 8 months; and it is agreed to make one payment of the whole: The time is required.

Ans. 6 months.

3. A man owes 1000 dols. whereof 200 dols. are to be paid at the present time, 400 dols. at 5 months, and the remainder at 10 months; but it is agreed to make one payment of the whole. Required the equated time. Ans. 6 months.

4. A man owes a certain sum of money* which is to be paid at four equal payments, viz. at 2 months, at 4 months, at 6 months, and at 8 months; but it is agreed to make one payment of the whole. Required the equated time. Ans. 5 months.

* When no particular sum is given, any sum may be assumed