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interest, take parts for the months and days, which add to the last year s interest, and the sum will be the interest required.

XX. REBATE, or DISCOUNT, IS the abating of so much on a debt, to be paid before it becomes due; which payment (rebate being deducted), if put out to interest for the same time, and rate per cent. per annum, would be equal to the sum first due.

RULE.

1. Find the interest of 100l. for the time given, and rate per cent. which interest add to 1001.

2. As that sum : is to the interest of 1001. or 100 :: so is the debt or sum proposed : to the rebate or present worth required. Or, subtract the rebate from the given sum, and the remainder will be the present worth, or money to be paid down.

EXAMPLES

per cent. ?

(1) What is the rebate of 420l. for 7 months, 6 days, at 5 per

cent. per annum? (2) What is the present worth of 100l. for 12 months, at 6 (3) What is the rebate and present worth of 6001. 10s. 6d.

payable in 10 months, at 4 per cent. per annum? (4) What is the discount of 890l. 165. being due July 27,

1807, this being December 12, 1800, at 5 per cent.

per annum? (5) Sold goods to the value of 4301 to be paid at two 4

months; that is, half at 4 months, and the other half at 8 months. What must be discounted for the present payment of the whole, discount being at 5 per

cent. per annum? (6) Suppose I have a legacy of 5501. left me on the 21st of

May, 1806, but not to be paid till Chistmas-day following; what is the present worth, discount allowed

at five per cent. per annum? (7) What is the present worth of 32201. payable as follows: 1001. at 3 months, 601. at 5 months, and the

remajnder at 6 months; discount at 6 per cent. per

annum ? (8) Sold goods to the value of 4001. to be paid at three 3

months, as follows : viz. first i, second ž, and the rest the third payment; what is the discount and pre

sent worth of the whole at 4 per cent. per annum? (9) What ready money will discharge a debt of 360l. due

at two 5 months; that is, į at 5 months, and the rest

at 10 months; discount at 3 per cent. per arnum? (10) What difference is there between the interest of 500l. at

5 per cent. per annum for 12 years, and the discount of the same sum, at the same rate, and for the same

time? (11) What ready money will discharge a debt of 133771.

13s. 4d. due two years, three quarters, 25 days hence; discount at 4} per cent. per annum ?

XXI. EQUATION OF PAYMENTS 1S when several debts are payable at different times, but it is mutually agreed, between debtor and creditor, that those several sums be all paid at once, and at such a time, as that neither party may be wronged thereby; this is called equating the time of payment. The common rule is as follows:

RULE.

Multiply the sum of each particular payment by its time, then add the products together, and divide the sum by the whole debt; the quotient, by this rule, is the equated time for the payment of the whole.

EXAMPLES.

(1) B. owes C. 6001. whereof 2001. is to be paid at 3 months,

1501. at 4 months, and the rest at 6 months; but they afterwards agreed the whole should be paid at once;

required the time. (2) A. bought of B. a quantity of goods which came to

4601. to be paid in the following manner, viz. 2001. at seven months, and the rest at five months; but after

wards they agree to make one payment of the whole.

I demand the equated time. (3) C. owes D. a certain sum, which is to be discharged in the

following manner, viz. } at three months, į in 4 months, and į at 9 months; but they afterwards agree to have but one payment of the whole: the equated

time is required. (4) A debt is to be discharged thus, viz. 4 present, at 4

months, į at 5 months, and the rest at 6 months ;

what is the equated time for the whole ? (5) E. is indebted to F. 2401. which by agreement is to be

paid at 5 months hence: but E. is willing to pay him 401. down, provided he will give him a longer time for the payment of the remainder, which is agreed on: the time of payment is required.

XXII. SINGLE FELLOWSHIP,

OR,

Fellowship without Time, IS when two or more persons join their stocks and trade together. To determine each person's particular share of the gain or loss, in proportion to his principal paid into the stock, observe the following

RULE. As the sum of the several stocks : to the gain or loss :: so is each person's share in the stock ; to his share of the gain or loss.

PROOF. Add all the shares together, and that sam, if right, will be equal to the whole gain or loss.

EXAMPLES. (1) Two merchants, A. and B. join in partnership: A. laid in

801. B. 60l. and they gain 281. What is each man's

share of the said gain? (2) Three persons, C. D. and E. trade together, and make a joint stock of 824l. and in three years' time they gained as much, and 701. over; C.'s stock was 3207. ! D's 3401. I demand E's stock, and what each person

gained by trading. (3) Suppose four merchants, A. B. C. and D. join their stocks

and trade together, of which A. puts in , B. j, C. , and D. }; but at the expiration of 12 months, they had the misfortune to Jose 1201. What must each

person suffer of the said loss? (4) Three merchants. D. E. and F. in partnership together,

with one common stock of 400l. gained as follows, viz. D. 301. E. 481, and F. 421. What was each man's

stock?
(5) Suppose the money and effects of a bankrupt amount to

24201. 17s. 6d. and he is indebted as follows, viz. to
A. 1000l. to B. 6401. to C. 9001. and to D, 8421. 16s.
How must his effects be divided amongst them? or
what share must each have?

QUESTIONS for Exercise at leisure Hours.
(6) A father ordered 500l. to be divided amongst his five

sons, thus. Give A. said he, }, B. \, C. }, D. Ž, and
E. 1. Part this equitably amongst them, according to

the father's intentions.
(7) Three persons purchase together a West-India sloop, to-

wards which A. advanced ž, B. 1, and C. 1401. How
much paid A. and B. and what part of the vessel had

C.?
(8) A. and B. clear by an adventure at sea 50 guineas, with

which they agree to buy a horse and chaise ;, whereof
they were to have the use in proportion to the sums
adventured, which was found to be A. 10; B. 7: they
cleared 45 per cent. What money did each send

abroad?
(9) A. and B. join their stocks, and vest them in brandy.

A.'s stock was 191. 19s. 8d, more than that of B. Now
by selling out their commodity at 55s. per anker, A.
cleared 741. 11s. and B. just 50 guineas. The quan-
tity of brandy dealt for is required, and the gain upon

the anker.
(10) In an article of trade A. gains 14s. 6d. and his ad-

venture was 35s. more than B.'s, whose share of the

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profit is but 8s. 6d. What are the particulars of their

stock? (11) Three persons, A. B. and C. entered into joint trade;

to which A. contributed 2101. B. 3121. They cleared 1 401. whereof 371. 10s. belongs of right to C. That person's stock and the several gains of the other two

are required. (12) A. and B. venturing equal sums of money, clear by joint

trade 1541. By agreement A. as to have 8 per cent, because he spent time in execution of the project, and B. was only to have 5. What was allotted A. for

his trouble? (13) A. B. and C. are three horses belonging to different men,

and are employed as a team to draw a load of wheat from Hertford for 30s. A, and B. are deemed to do of the work, A. and C. , and B. and C. 1 of it: they are to be paid proportionably. Do you know how to

divide it as it should be? (14) Bought 100 quarters of malt, meal, and oatmeal, toge

ther, for 1421. For every 5 bushels of malt I had 3 of meal; for every 8 of meal I had. 7 of oatmeal. What did these cost me severally per bushel, the malt being half as dear again as the meal, and the meal being

double the price of the oatmeal ? (15) In raising a joint stock of 4001. A. advanced *

of }, C. more the difference between A.'s adventure and B.'s; and D. the rest of the money. What did every one subscribe ?

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XXIII. DOUBLE FELLOWSHIP,

OR,

Fellowship with Time, IS when each person's stock continues unequal time in company, so that a consideration must be made of the time, as well as of the stock.

RULE. Multiply each person's stock by the time it has continued in trade, and proceed with the producte, as with the particular stocks in Single Fellowship.

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