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Any sumn, at simple interest, will double itself in 16 years 8 months; but al compound, in a little more than half that time; that is, in 11 years, 8 months and 22 days. Hence, we see that there is considerable difference in a few years, and when compound interest is permitted to accumulate for ages, it announts to a sum almost incredible. If 1 cent had been put at compound in terest at the coinmencement of the Christian era, it would have amounted, at the end of the year 1827, to a sum greater than could be contained in six millions of globes, each equal to our earth in magnitude, and all of solid gold, while the simple interest for the same time would have amounted to only about one dollar. The following question is inserted, more for the sake of ex emplifying the preceding statement, than for the purpose of its solution. The amount, however, at compound interest, may be found, without much perplexity, by ascertaining the amount of 1 cent for 20 years, fo'ind by the Table, ihen making this amount the principal for 20 years more, and so on for the whole number of years.

16. Suppose 1 cent had been put at interest at the commencement of the Christian era, what would it have amounted to at simple, and what at com. pound interest, at the end of the year 1827? A. Simple, $1,106 1%; com pound, $172616474047552529470760914974711959976620354 % nearly.

EQUATION OF PAYMENTS.

| LXXII. Q. What is the meaning of equation ?
A. The art of making equal.
Q. What is equation of payments ?

Ă. It is the method of finding an equal or mean time for the payment of debts due at different times.

1. In how many months will $1 gain as much as $2 will gain in 6 months? A. 6 X 2= 12 months.

2. ow long will it take $1 to gain as much as $5 wil gain in 12 inonths? A. 60 months.

3. How many months will it take $1 to be worth as much as the use of $10, 20 months ? A. 200 months.

4. A merchant owes 2 notes, payable as follows: one of $8, to be paid in 4 months; the other of $6, to be paid in 10 months : but he wishes to pay both at once : in what time ought he to

pay them?

4 X8=32; therefore, $8 for 4 mo. =$1 for 32 mo., and 10 x 6 60; therefore, $6 for 10 mo.= $1 for 60 mo.

12

92

Therefore, he might have $1,92 months; and he may keep $14, Il part as long; that is, I'd of 92 months, which is 12 = 14,=6 mo. 1314 da., Ans.

Q. Hence, to find the mean time of payment, what is the

RULE? A. Multiply each payment by the time, and the sum of these several products, divided by the sum of the payments, will be the answer.

Note.—This rule proceeds on the supposition, that what is gained by keep ing the money atter it is due, is equal to what is lost by paying it before it is due. But this is not exactly true, for the gain is exfual to the interest, while the loss is equal only to the discount, which is always less than the interest. However, the error is so triling, in most cases which occur in business, as pot Lo make any material ditference in the result.

5. A owes B $200 to be paid in 6 months, $300 in 12 months, $500 in 3 months; what is the equated time for the payment of the whole ? A. 67.

6. What is the equated time for paying $2000, of which $500 is due in 3 months, $360 in 5 months, $600 in 8 months, and she balance in 9 months? A. 6206 = 6 months.

7. A merchant owes $600, payable as follows: $100 at 2 months, $200 at 5 months, and the rest at 8 months : but he wishes to pay the whole debt at one time : what is the just time for said payment? A. 6 months.

8. I owe as follows, viz. to A $1200, payable in 4 months; to B $700, payable in 10 months; to C $650, payable in 2 years; 6 D $1000, payable in 34 years; to E $1 270, payable in 20 months ; and to F $500, payable in 4 years ; now, what would be the equatea time for paying the whole ? A. 22months.

Questions on the foregoing. 1. A man bought a barrel of flour for 2£. 15 s. 6 d., a hhd. of molasses for 6£. 15 8., and a barrel of brandy for 8£. 15 8.; what did the whole cost? A. 18£. 5 8. 6 d.

2. Wat wili 9600 yards of cloth cost, at $50 a yard?-4800. At $,33} :-3200. At$,25 ?-2400. At PCU ?-19920. At $,163 ?1600. At $,124 ?-1200. At $,64?-C00. At $,52-480.

A. $16200. 3. What is the product of 2 s. 6 d. multiplied by 22-5. By 42-10. By, 77-17-6. By 10 ?-1-5. By 12-1-10.

A. 4£. 78.6d.

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4. Divide 21£. 19 s. 9 d. equally among 6 men.

A. 3£. 13 s. 3) d 3. Reduce }, , and }, to the least common denominator.

A. 16, 18, 6. Change 2000 francs to federal money. A. $375.

%. Iš go+,so +673 + Toodoo. A. 673,37505. 18. Change 4500£. English or sterling money, to dollars of 48. 6 d. each. A. $20,000.

9. What is the interest of $21,20 for 6 months ?-636. For? months 15 days ?-371. For 10 month ?-159. For 10 days?-35 For 5 days ?-17. For 4 days ?-14. A. $1,232 t.

10. What is the amount of $300, at 7 per cent., for 1 year:321. At 3 per cent. ?-309. At 54 per cent. ?-31650. per cent.?-32925. At 124 per cent. ?-33750. A. $1613,25.

11. What is the discount of $315 for 10 months, at 6 per cent. ?-15. Of $550 for 1 yr. 8 mo. ?-50. of $2660 for 5 yrsi 6 mo.?-660. Of $121,402 for 8 yrs. 4 mo. 15 da. 2-40602.

A. $765,602. 12. What is the compound interest of $560 for 4 yrs. ?-146987 For 2 yrs. 6 mo.?-88002. For 3 yrs.?-106968. A. 342,047.

13. A merchant bought goods amounting to $368,925 ready money, and sold them again for $488,75, payable in 2 yrs. mo.; how much did he gain, discounting at 6 per cent. ? (Find the present worth of $488,75 first, then subtract to find the gain.)

A. $56,075. 14. Bought corn for $,60, and sold it for $,72; what was thic gain per cent.?. A. 20 per cent.

15. Bought 40 ga’lons of molasses, at 27 cents a gallon; but, by accident, 4 gallons leaked out; at what rate must I sell the remainder, per gallon, to lose nothing? and how much to gain on the whole cost 20 per cent. ?

A. 30 cts.; and, to gain 20 per cent., 36 cts

RULE OF THREE,

OR

SIMPLE PROPOKTION,

(LXXIII. 1. What will 3 yds. of cloth come to at 20 cents a yard? What will 5 yards? Will 7? 8? 12}

2. If 2 gallons of molasses cost 50 cents. what will 3.gal lons costă (Find what one gallon will cost first. It is 25

cents. Then, 3 gallons are 3 times 25,=75 cents. Pro ceed in the same manner with other suins of like nature.) What will 5 gallons cost? What will &?

3. If 4 lbs. of sugar cost 48 cents, what will 2 lbs. cost? (Find what 1 lb. will cost first.) What will 6 lbs. cost ? What will 8? What will 12? What will 20?

4. If 2 bushels of corn cost a dollar, how much is it a bushel ? What will 3 bushels cost? What will 4? What will 6? What will 8?

5. If 20 yards of cloth cost 60 cents, how much is it a yard? What will 6 cents buy? Will 18 cents buy? Will 80 cents? Will 90 ? Will 300 ?

6. How many ponnds of cheese will 12 cents buy, if 4 lbg. cost 48 cents? How many will 24 cents buy? How many will 60 cents? How many will 108 cents?

7. If 4 dollars buz 2 barrels of cider, how many barrels will 6 dollars buy? (Find the value of 1 first.) How many will 8 dollars buy? How maliy will 12? How many will 24? How many will 36 ? How many will 48? How many will 60? How many will 100? How many will 150 ? How many will 300? How many will 400? How many will 500 How many will 800?' How many will 2000 ? How many will 3000? How many will 10000 ?

8. If you pay 16 cents for 4 oranges, how many cents will buy 6? Ilow many 36? How many 48? How many our

9. If 100 oranges cost 400 cents, how many cents will 4 cost? What will 8 cost? What will 25 cost? What will 80 cost? What will 50 cost?

10. If 4 tons of hay will keep 2 cattle over the winter, how many tons will keep 6 cattle the same time? How many 8? How many 10? How many 20? How many 40 ? How many 60 ? How many 80 ?

11. If 500 cattle eat 1000 tons of hay in one winter, what will 2 cattle eat? What will 3? What will 5? What will 20 ? What will 50? What will 200?

12. If 2 penknives cost 25 cents, what will 3 cost? What will 4? What will 8? What will 12? What will 16?

13. If you pay 26 cents for 2 inkstands, how inany cents will buy 3? Will buy 4? 5? 6? 7? 8? 9? 10? 20? 30 ? 40 ?

14. If z of a yard of broadcloth cost 4 dollars, what will

cost? (ir z cost 4 dollars, will cost 2 dollars.) What will *? Wha &? What ? What ? What 10? What

13? What 13? What 1$? What 15? What if? What 2 yards ? What g? (If g make 1 yard, then I yard and } are ..) What will be of a yard cost? What 11? What ?? What? What ? What 3 yards ?

15. The interest of 100 dollars for 1 year is 6 dollars, at 6 per cent. ; what is it for 2 years ? For 3? For 5? For 7? For 9? For 12? For 20?

16. If 6 men can do a piece of work in 12 days, how long will it take 1 man to do the same? (1 man will be six times as long as 6.) How long will it take 2 men? (2 men will do it quicker than 1 man.) 3 men? 12 men ?

17. If 4 men build a wall in 20 days, how many men would it require to build the same in 40 days? (d aš many men.) In 80 days ?

After the same manner perform the following

Exercises for the Slate. 1. If 20 yards of cloth cost $40, what will 8 yards cost ? 1 yard is at of $40; that is, 40 +20=$2 a yard; then 8 yards are 8X2= $16, Ans.

2. What can you buy 15 tons of hay for, if 3 tons cost $36? (Find what 1 ton will cost first.). A. $180.

3. If 2 bushels of oats cost 40 cents, what will 24 bushels cost? A. $4,80. 4. What will 25 lbs. of sugar cost, at 17 cents a pound?

17 x 25=$4,25, Ans. 5. If $4,25 buy 25 lbs. of sugar, how much is it a pound?

A. 17 cents. 6. If 3 pair of shoes cost $4,50, what will 12 pair cost ?-18 What will 8 ?-12. What will 15-2250. What will 16 ?-24

A. $76,50. 7. If 2 pair of stockings cost 50 cents, what will 3 pair cost 2 75. What will 15 ?-375. What will 25 ?-625. What will 80 ?-20. What will 96 2-24. What will 267 ?-6675.

A. $121,50. 8. What will 600 bushels of rye cost, at 84 cents a bushel ? 504. What will 107-840. What will 40 ?-3360. What will 800:-672. What will 1090 ?-840. What wilt 27-168.

A. $2059,68 9. If 60 cents buy 4 lbs. of tobacco, how much will 30 cents buy ?-2. How much will 90 cents ?-6. How much will 120 cents ?-0. How much will $2,10 ?-14. How much will $2,40. 16. A. 46 lbs

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