TABLE,

Showing the amount of 1€, or $1, for 20 years, at 5 and 6 per cent., at compound interest.

14. What is the compound interest of $20,15 for 4 years. at 6 per cent.?

By the Table, $1, at 6 per cent. for 4 years, is $1,26247, × $20,15= $25,438, amount, from which $20,15 being subtract ed, leaves $2887% +

15. What is the amount of $10,50, at 5 per cent for 2 years? (115762) For 6 years? (140709) For 8 years? (155132) For 15 years? (218286) For 17 years? (240661) For 20 years? (278595). $114,914+, A.

Any sum, at simple interest, will double itself in 16 years 8 months; but at 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 imounts to a sum almost incredible. If 1 cent had been put at compound interest at the commencement 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 mutions of globes, each equal to our earth in magnitude, and all of so.id go.d, while the simple interest for the same time would have amounted to on.y about one dollar. The following question is inserted, more for the sake of exemplifying the preceding statement, than for the purpose of its solution. The amount, however, at compound interest, may be found, without much perplex.ty, by ascertaining the amount of 1 cent for 20 years, found by the Table, then 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 commencemert of the Christian era, what would it have amounted to at simple, and wht at combound interest, at the end of the year 1827? A. Simple, $1,1062; compound $1726164740475525294707609149747119599766203545

nearly,

C

a

EQUATION OF PAYMENTS.

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

Q. What is equation of payments? A. It is the method of firding 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 wil? gain in 6 months? A. 6x2= 12 months.

2. How long will it take $1 to gain as much as $5 will gain in 12 months? 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 X 8=32; therefore, $8 for 4 mo. = 10 × 6= 60; therefore, $6 for 10 mo. =

14

$1 for 32 mo., and $1 for 60 mo.

92

Therefore, he might have $1, 92 months, and he may keep $14, part as long; that is, 1 of 92 months, which is 9214,6 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 after 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 equal to the interest, while the loss is equal only to the discount, which is always less than the interest However, the crror is so trifling, in most cases which occur in business, as not to make any material difference 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. 6.

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 the balance in 9 months? A. 661 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 ↳ D $1000, payable in 34 years to E $1270, payable in 20

1

months; and to F $500, payable in 4 years; now, what would be the equated time for paying the whole? A. 22138 months

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 s., and a barrel of brandy for 8£ 15 s.; what did the whole cost? A. 18£ 5 s. 6 d.

2. What will 9600 yards of cloth cost, at $,50 a yard? (4800) At $,33? (3200) At $,25? (2400) At $,20? (1920) At $,163? (1600) At $,12? (1200) At $,64? (600) At $,5? (480) A. $1200.

3. What is the product of 2 s. 6 d. multiplied by 2? (5) By 4? (10) By 7? (17-6) By 10? (1-5) By 12? (1-10) A. 4£ 78. 6 d.

4. Divide 21£ 19 s. 9 d. equally among 6 men? 3 d.

A. 3£ 13 s

5. Reduce,, and, to the least common denominator. A. 18, 28, 28.

6. Change 2000 francs to federal money. A. $375

7. +380 +,3+ 1880 +673 +100000. A. 673,37505. 8. Change 4500£. English or sterling money, to dollars of 4s 6 d. each. A. $20000.

9. What is the interest of $21,20 for 6 months? (636) For 3 months 15 days? (371) For 1 month? (159) For 10 days' (35) For 5 days? (17) For 4 days? (14) A. $1,23 2+.

10. What is the amount of $300, at per cent., for 1 year? (321) At 3 per cent.? (309) At 5 per cent.? (31650) At 99 per cent.? (32925) At 125 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 yrs. 6 mo.? (660) Of $121,402 for 8 yrs. 4 mo. 15 da.? (40602) A. $765,602.

12. What is the compound interest of $560 for 4 yrs.? (146987) For 2 yrs. 6 mo. (88092) 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. 6 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 the gain per cent.' 4. 20 per cent.

15. Bought 40 gallons 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 ets.; and, to gain Wzer cent., 36 ets.

RULE OF THREE,

OR

SIMPLE PROPORTION.

↑ 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 gallons cost? (Find what 1 gallon will cost first. It is 25 cents. Then 3 gallons are 3 times 25, =75 cents. Proceed in the same man ner with other sums of like nature.) What will 5 gallons cost? What will 8?

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? Wat vill 8? What will 12? What will 20?

4. If 2 bushels of corn cost a dollar, how much is it a bushd 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 30 cents Will 90? Will 300 ?

6. How many pounds of cheese will 12 cents buy, if 4 lbs. cost 48 cents? How many will 24 cents buy? How many wil 60 cents? How many will 108 cents?

How

7. If 4 dollars buy 2 barrels of cider, how many barrels will 6 dollars buy?(Find the value of 1 first.) How many will 8 dollars buy? How many will 12? How many will 24 ? 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 wil. 800? How many will 2000 ? How many will 3000 ?

many will 40000

Ho

8. If you pay 16 cents for 4 oranges, how many cents wil buy 6? How many 36? How many 48? How many 60? 9. If 100 oranges cost 400 cents, how many cents will 4 cost? What will 25 cost? What will 30 cost?

What will 8 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?

many 60? How many 80 ?

How many 40 ?

Ho

11. If 500 cattle eat 1000 tons of hay in one winter, what will 2 cattle eat? What will 3? What will 5? What wi.. 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 many cents will 5? Will buy 4? 6 ? 7? 8? 9? 10? buy 3? 30? 40?

20 ? 14. If of a yard of broadcloth cost 4 dollars, what will cost? (If cost 4 dollars, will cost 2 dollars.) What will ? What? What? What? What 1? What 1 What 18? What 1? What 1 What 1? What 2 yards What? (If make 1 yard, then 1 yard and are .) Wha! will of a yard cost? What? What? What 16. What? What 3 yards?

15. The interest of 100 dollars for 1 year is C dollars at € per cent.; what is it for 2 years? Fɔ 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 6 times as long as 6.) How long will it take 2 men? it quicker than 1 man.) 3 men? 12 men?

(2 men will do

17 If 4 men build a wall in 20 days, how many men would it require to build the same in 40 days? ( as many men.) In 60 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 of $40; that is, 40 ÷ 20=$2 a yard; then, 8 yards are 8 X2=$16, Ans.

2. What can you buy 15 tons of hay for, if 3 tons cost $36: (Find what I 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? What will 15? (375) What will 25? (625) What wil 80 (20) What will 96? (24) What will 267? (C675) A. $121,50.

(75)

8. What will 600 bushels of rye cost, at 84 cents a bushel? 504) What will 10 (840) What will 40? (3360) What