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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 ?

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 960245.

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 2

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Ans. at 3 months. 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 suin may be assumed

5. A man bought a quantity of goods, to pay at the end of every 3 months, till the whole was paid ; but it is agreed to make one payment of the whole. Required the equated time.

Ans. 6 months. 6. A debt of 420 dols. is due at the end of 6 months, but the debtor will pay 60 dols. now, provided the rest may be forborne a longer time, which is agreed on. Required the time.

dols. 420. Paid present,

60

months. Remains,

360 :
: 6 :: 420

6

3

360)2527067 months, Ans.

252

Note. In the 6th example, it is evident that if part is paid now, the remainder ought to be foróorne a longer time. See the stating, agreeably to the general method of stating the Rule of Proportion.

DISCOUNT.

Discount is an allowance made for the payment of a sum of money before it becomes due, and is the difference between the sum due, at a time to come, being specified and the sun which ought to be paid at the present time, (called the present worth) which if put to interest would amount to the given sum at the time specified.

Discount is also sometimes allowed on depreciated money, such as foreign coin, the bills of some banks, &c ; in this case it is commonly at so much per cent ; in the former case so much per cent. per annim.

CASE 1. To find the discount on a sum of money payable on a future day,, provided the same be paid at the present time; the sun and rate of discount being given.

RULE 1. As 12 months, or 365 days, are to the rate per cent, so is the time proposed, to a fourth number, or sum.

2. Add that fourth number, or sum, to 100 pounds, or 100 dollars, (as the given sum may be.)

3. As this last sum is to the fourth number, so is the given sum to the discount.

EXAMPLES 1. Required the discount of £795 11 2, for 11 months, at 6 per cent. per annum ? 12 : 6 :: 11

6

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2. What is the discount of dols. 9356,25, for 2 years and 5 months, at 5 per cent. per annum ?

Ans. dols. 1008,65,6+ 3. What is the discount of dols. 957,26, for 7 months, at 6 per cent. per annum ? Ans. dols, 32,37,17

CASE II. To find the present worth of a given sum, payable at a future day, having the rate per cent given.

RULE. Proceed as directed in Case I, till the fourth number or sum is found and added' to 100; then say, as that sum is to 100, so is the given sum to the present worth ; or, find the discount as directed in the ist Case, and subtract it from the given sum ; the remainder will be the present worth.

EXAMPLES. 1. Required the present worth of £795 11 2, for li months, at 6 per cent. per annum. 12 : 6 :: 11

11
12)66
5 5 or £5 10

100
105 10 : 100 :: 795 11 2
20

20
2110

15911 12

12 25320

190934

100
2532|0)
1909340|0(£754 1 89 5. Ans.
17724

This proves the first example in
13694 Case 1.
12660
10340 Or, thus, From
10128 the given sum £795 11 2
212 Subtr. discount,
20 Found by Case I

41 9,54 15

1572 4240 Example 1, 2532 Remains the

96 1708

present worth, 12 20496 20256 240

4 960

754 1 822832

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