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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.
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 1007. 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.
(1) What is the rebate of 4201. for 7 months, 6 days, at 5 per cent. per annum ?
(2) What is the present worth of 100l. for 12 months, at 6 per cent.?
(3) What is the rebate and present worth of 600l. 10s. 6d. payable in 10 months, at 4 per cent. per annum? (4) What is the discount of 8907. 16s. 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 550l. 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: 100l. at 3 months, 601. at 5 months, and the
remainder at 6 months; discount at 6 per cent. per annum?
(8) Sold goods to the value of 400l. to be paid at three 3 | months, as follows: viz. first, second, and the rest the third payment; what is the discount and present 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, at 5 months, and the rest at 10 months; discount at 3 per cent. per ar.num? (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 43 per cent. per annum ?
XXI. EQUATION OF PAYMENTS
IS 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:
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.
(1) B. owes C. 600l. whereof 2001. is to be paid at 3 months, 150%. 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 460l. 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, in 4 months, and 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. present, at 4 months, at 5 months, and the rest at 6 months; what is the equated time for the whole?
(5) E. is indebted to F. 240l. which by agreement is to be paid at 5 months hence: but E. is willing to pay him 40l. 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,
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.
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.
Add all the shares together, and that sum, if right, will be equal to the whole gain or loss.
(1) Two merchants, A. and B. join in partnership: A. laid in 80%. B. 60l. and they gain 287. 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 8241. and in three years' time they gained as much, and 70l. over; C.'s stock was 3201. D.'s 340l. 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 2, B., C. I, and D.; but at the expiration of 12 months, they had the misfortune to lose 120l. 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. 30l. E. 481. and F. 427. What was each man's stock?
(5) Suppose the money and effects of a bankrupt amount to 2420l. 17s. 6d. and he is indebted as follows, viz. to A. 1000l. to B. 640l. to C. 900l. and to D. 8427. 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. †, and E. Part this equitably amongst them, according to the father's intentions.
(7) Three persons purchase together a West-India sloop, towards which A. advanced, B. 4, and C. 140l. 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
(9) A. and B. join their stocks, and vest them in brandy. A.'s stock was 197. 19s. 8d. more than that of B. Now by selling out their commodity at 55s. per anker, A. cleared 742. 11s. and B. just 50 guineas. The quantity of brandy dealt for is required, and the gain upon the anker.
(10) In an article of trade A. gains 14s. 6d. and his adventure was 35s. more than B.'s, whose share of the
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 210l. B. 312l. They cleared 140l. whereof 377. 10s. belongs of right to C. 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. was 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. 3, and B. and C. 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, together, for 1427. 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 400. A. advanced ✯, B. 11⁄2 13 of, C. more the difference between A.'s adventure and B.'s; and D. the rest of the money. What did every one subscribe?
XXIII. DOUBLE FELLOWSHIP,
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.
Multiply each person's stock by the time it has continued in trade, and proceed with the products, as with the particular stocks in Single Fellowship.