There is another method of computing interest when the time consists partly or wholly of determinate fractions, which will probably be found as short and simple as either of those already given, namely, by the method called " Practice,” as developed p. 254. Or, the time may be resolved into its lowest denomination, and the whole calculated by one operation. Two examples by each of these methods will make both sufficiently clear. 1. Find the interest of $265 for 2 years and 5 months, at 7 per cent. I. By Practice. 14 =product of years and rate. 37 10 =Int. for 2 y. 4 m.=d of 2 y 6.183=Int. for 1 m.= 1 of 4 m. 1.545 Int. for $44.828=Int. for 2 y. 5 m. 4 m. 1 m. II. By changing the time to its lowest denomination. 2 y. 5 m.= -29 months. m. r. Tão of principal 2.65 x 29X7-12=2. 203 =2 y 5 m. 2. Find the interest of $224.75 for 3 years, 4 months, and 16 days, at 5 per cent. I. By Practice. 15=product of years and rate. 3367125=Int. for 3 y. 4 m. 5 of 3 y 347458=Int. for 15 d. of 4 m. 14683=Int. for 15 d. 1 d. ijs of 15 d. «0312=Int. for 1 d. $3769578=Int. for 3 y. 4 m. 16 d. 4 m. II. By changing the Time to its lowest denomination. 3 y. 4 m. 16 days =1216 X5 rate=6080. 6080 $2'2475=ido of principal. 152 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. part of the - by the I. For one or more years. RULE.— Multiply the and the , or by their product. II. For fractional parts of years. per cent. RULE.— Multiply the by of the time when it consists of months, and by of the time when it consists of days. 2. When the rate is less or more than 6 per cent. RULE.— Multiply the part of 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 per cent. per annum. years, at 5 500 principal lent. 26-25 interest on $525 for 1 year. 27656 interest on $551-25 for 1 year. Amount 578.81 principal at the end of 3 years. 500 original principal. 78-81 Compound Int. on $500 for 3 years. 2. Find the amount of $324 at compound interest, for 4 years, at 6 per cent. per annum. Ans. $409.04. 3. Find the amount of $532'24 at compound interest for 54 years, at 4 per cent. per annum. Ans. $654.02. 4. Find the amount of the same sum at compound interest for 24 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. $3-75. 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? D Five cows for 4 months=1 cow for 20 months. Ans. A $1875; B $6-25; C $1250; 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 ? Do 600 for 6 months=3600 for 1 month. Ans. A's loss $12739; B's $9131; C's 81%. 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 have $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? 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 $3853388, B's $666,2888 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. What was the whole gain, and the gain of each ? Ans. Whole gain £315 5s. Gain of A, £100 58.; of B, £127 15s; of C, £87 5s. 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 $184,13, B $1531}, C $16175. EXCHANGE $ 1 1. Change £5 12s. sterling to federal money. $ 5-6 decimal of £5 12s. =$249, Ans. 2. Change the same sum from New England currency, and also from New York currency, to dollars. 3. Change $184 to New England currency, and $14 to New York currency. 4. Change $36-50 to New York currency. 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? £2000.106 2120 =$94223, Ans. 225.100 "225 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 cotton by the same vessel, which brings the same sum. 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. How much should he be credited in New Orleans, if Louisiana funds be at a discount of 2 per cent. ? Ans. $2426-30. |