II. By changing the Time to its lowest denomination. 3 y. 4 m. 16 days =1216×5 rate=6080. 6080152 $2.2475= of principal. 9)341.6200 379577+=Int. for 3 y. 4 m. 16 d.=1216 d. Perform all the exercises under the head of "Short Processes," &c., where the time is of two or three denominations, first by "Practice," and then by "Changing the Time," as above. RECAPITULATION OF THE ABRIDGED PROCESSES FOR THE CALCULATION OF SIMPLE INTEREST. I. For one or more years. RULE.-Multiply the part of the by the or by their product. II. For fractional parts of years. 1. When the rate is 6 per RULE.- Multiply the part of the when it consists of months, and by consists of days. cent. by and the -, of the time of the time when it 2. When the rate is less or more than 6 per cent. RULE.- Multiply the part of the by the lowest term of a fraction, whose numerator consists of the product of the and the —, and whose denominator is 12 for months and 360 for days; or, by "Practice," or by "Changing the Time." COMPOUND INTEREST. Definition.-Compound Interest is that which arises from the principal increased by the interest as it becomes due at the end of each year, or other stipulated time of payment. Though, no doubt, strictly just, it is illegal in most countries, most probably on the principle that it is well to encourage frequent settlements, and to discourage the accumulation by con stant increase of unpaid interest, which might finally be injurious both to debtor and creditor. 1. Find the amount and interest of $500 at compound interest for 3 years, at 5 per cent. per annum. 500 25 525 principal lent. principal at the end of 1 year. 26-25 interest on $525 for 1 year. 551.25 principal at the end of 2 years. 27.56 interest on $55125 for 1 year. Amount 578 81 principal at the end of 3 years. 78-81 Compound Int. on $500 for 3 years. Ans. $409.04. 2. Find the amount of $324 at compound interest, for 4 years, at 6 per cent. per annum. 3. Find the amount of $532-24 at compound interest for 51 years, at 4 per cent. per annum. Ans. $654'02. 4. Find the amount of the same sum at compound interest for 21 years, at 6 per cent. Ans. $615'96. Another method for computing compound interest will be developed in the Supplement, under the head of "Progression by Ratios." PARTNERSHIP. 1. Six villagers hired a pasture for $75. A put in 5 cows for the season, B 2, C3, D 8, and E and F 1 each. How much was the pasturage for each cow? Ans. $375. 2. The same men the following year hired the same pasture for the same price. A put in 5 cows for 6 months; B 2 cows for 5 months; C 5 for 4 months; D 8 for 5 months; and E and F 2 each for 5 months. How much had each person to pay? Five cows for 4 months-1 cow for 20 months. Ans. A $18.75; B $6.25; C $12.50; D $25; E and F $6.25 each. 3. Four men enter into partnership. A puts in $2500, B $3000, C $2500, and D $2000. They gain $1500. What is the share of each? Ans. A $375, B $450, C $375, and D $300. 4. Three men enter into partnership. A puts in $500 for 10 months, B $600 for 6 months, and C $800 for 4 months. They lose $300. How is this loss to be apportioned ? 600 for 6 months-3600 for 1 month. Ans. A's loss $1277; B's $913; C's 812. 5. Two merchants traded in company. Each put in $500. But A kept his in for 12 months, while B was only in for 6 months. Their gain was $600. How should it be divided? Ans. A should hạve $400, B $200. 6. A, B, and C, put money into a joint stock. A put in $40, B and C together $170. They gained $126, of which B took $42. What did A and C gain, and B and C put in respectively? 248 2508. Ans. A gained $24 and C $60; B put in $70 and C $100. 7. Two merchants entered into partnership for 18 months. A, at first, put into stock $400, and at the end of 8 months put in $200 more. B, at first, put in $1100, and at the end of 4 months took out $280. At the expiration of the 18 months they found the gains to amount to $1052. What is each man's share? Ans. A's $3852260, B's $666,24 8. A and B went into partnership. A put in on the first of January £150, but B could not put in any till the first of May. What did he then put in to have an equal share at the year's end? Ans. £225. 9. Three merchants traded in company. On the first of January they reckoned their gains, of which A and B took £228; B and C £215; and A and C £187 10s. the whole gain, and the gain of each ? Ans. Whole gain £315 5s. £127 15s; of C, £87 5s. What was Gain of A, £100 5s.; of B, 10. Three merchants, A, B, C, enter into partnership. A advances $1200; B $800, and C $600. A leaves his money 8 months, B 10 months, and C 14 months, in the business. They gain $500. What is the share of each? Ans. A receives $184, B $15311, C $16173. EXCHANGE. 1. Change £5 12s. sterling to federal money. 5.6 decimal of £5 12s. T225 decimal of $1 in pounds. =$248, Ans. 2. Change the same sum from New England currency, and also from New York currency, to dollars. 3. Change $18 to New England currency, and $14 to New York currency. 4. Change $36.50 to New York currency. 5. Change £14 12s. New York currency to dollars. 6. A merchant sends cotton to England, which is sold there for £2000, besides paying all expenses. To a friend, who wishes to purchase goods in England, he sells a draft for that amount at 6 per cent. advance. How many dollars does he receive for his draft? 7. A merchant of Newbern, N. C., bought goods in New York to the amount of $1000. He directed the seller to draw on him through the Planter's Bank of Charleston, S. C., in the currency of that state. What must be the amount of the New York merchant's draft, when South Carolina money was at 2 per cent. discount in New York, and how much must the Newbern merchant pay in North Carolina currency, exchange with Charleston being 1 per cent. discount only? Ans. £238'09+ in S. Carolina, and £412·35+ in N. Carolina currency. 8. A merchant in New York ships a quantity of cotton to Liverpool, which sells for £500, besides paying freight, commission, and all other expenses. For how many dollars should he sell his bill of exchange on Liverpool, exchange being 7 per cent. advance ? Ans. $2377 77. 9. Another merchant sends which brings the same sum. cotton by the same vessel, But, instead of selling his bill in New York, he forwards it to a merchant in New Orleans, in payment for a debt which he owes him. be credited in New Orleans, if Louisiana count of 2 per cent.? How much should he funds be at a disAns. $2426 30. 10. A merchant in Boston has effects at Amsterdam, Holland, to the amount of $3530, which he can remit by way of Lisbon at 840 rees per dollar, and thence to Boston at 8s. 1d. per milree (1000 rees); or, by way of Nantz, at 5 livres per dollar, and thence to Boston at 6s. 8d. per crown of 6 livres. Which is the most advantageous way of remittance, and what is the difference between them? Ans. By Lisbon £1198 8s. 8d. By Nantz £1059. 11. If 140 braces at Venice be equal to 150 braces at Leghorn, and 7 braces at Leghorn be equal to 4 American yards: how many American yards are equal to 524 Venetian braces? Ans. 32 yards. 12. If 40 lb. at Newburyport make 36 at Amsterdam, and 90 lb. at Amsterdam make 116 at Dantzick, how many lb. at Dantzick are equal to 244 at Newburyport? Ans. 283 lbs. 13. A merchant in Mississippi purchases goods to the value of $1500 from a merchant in New York. He sells the goods in his store at Jackson, and receives his pay in cotton, which he sends to his correspondent in New Orleans, who forwards it to Liverpool, where it is sold, and the net proceeds remitted to a banker in London, and placed to the credit of the Mississippi merchant. For how much sterling money must the latter draw a bill of exchange on London in favor of the New York merchant, allowing him 3 per cent. interest for the credit on his goods, exchange on London being 7 per cent. advance? Ans. £324 17s. 73d. 14. A banker received 759 ducats at 7s. 6d. per ducat, and 579 dollars, at 4s. 8d. per dollar, which he exchanges for Flemish marks, at 14s. 3d. each. How many ought he to receive? Ans. 589 15 171. 15. A bill of exchange for £400 sterling was accepted at London, for an equal value delivered at Amsterdam, at £1 13s. 6d. Flemish, for £1 sterling. How much money was delivered at Amsterdam ? Ans. £670 Flemish. 16. A merchant delivered at London £120 sterling, to receive £147 Flemish in Amsterdam. How much was £1 sterling valued at in Flemish money? Ans. £1 4s. 6d. 17. A factor sold goods at Cadiz for 1468 pieces of eight, valued at 4s. 6d. sterling each. How much sterling money do those pieces of eight amount to? Ans. £333 7s. 2d. 18. A traveller wished to have an equal number of crowns, |