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10. What is the difference between the simple interest of $200 for 3 years, and the compound interest for the same time?

A. $2,2031% 11. What is the compound interest of $600 for 2 years 6 months ?

In calculating the compound interest for months and days, first find the amount for the years, and on that amount calculate the interest for the months and days; this interest, added to the amount for the years, will be the interest required.

A. $$94,38,4+. 12. What is the compound interest of $500 for 3 yrs. 4 mo.?

A. $107,41816+ 13. What is the difference between the simple and compound interest of $200 for 3 yrs. ?-22032. For 4 yrs. 6 mo.?-60702. For 2 yrs. 8 mo. 15 da. ?-17706. A. $10,044.

As the amount of $2 is twice as much as $1, $4, 4 times as much, &c., hence, we may make a table containing the amount of the l£, or $1, for -Beveral years, by which the amount of any sum may be easily found for the

same time.

Years.

Years

TABLE,
Showing the amount of 1£, or $1, for 20 years,

at 5 and 6 per
cent., at compound interest.
5 per ceni. 6 per cent.

5 per cent. 6 per cent. 1

1,05000 1,06000 11 1,71033 1,89829 2 1,10250 | 1,12360 12 1,79585 2,01219 3 1,15762 1,19101 13 1,88564

2,13292 4 1,21550 | 1,26247 14 | 1,97993

2,26090 5 1,27628 | 1,33822 15 2,07892 2,39655 6 1,34009 1,41851 16 2,18287 2,54035 7 1,40710 | 1,50363 17 | 2,29201 | 2,69277 8 1,47745 | 1,59384 18 2,40661

2,85433 9 1,55132 1,68947 19 2,52695 3,02559

10 1,62889 1,79084 20 2,65329 3,20713 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, X $20,15= $25,438, amount, from which $20,15 being subtracted, leaves $5,28810 +:

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.

$114,91410 +, Ans.

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 month and 22 days. Hence, we see that there is considerable difference in a fie years, and when compound interest is permitted to accumulate for ages, it amounts 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 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 exemplifying 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, found by the Table, then making this amount the principal for 20 years more, and so on for the whole number of

years. 16. Surpose 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 compound interest, at the end of the year 1827? A. Simple, $1,106%; compound, $172616474047552529470760914974711959976620354,

56 107

nearly.

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 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. 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

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

14

92

pay them?

Therefore, he might have $1, 92 months ; and he may keep $14, T'E part as long; that is, it of 92 months, which is 92 - 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 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 error 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 tiine for the payment of the whole ? A. 610.

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. 6:296 = 62 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; to D $1000, payable in 3 years; to E $1270, payable in 20 months ; and to F $500, payable in 4 years ; now, what would be the equated time for paying the whole ? A. 223357 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 $,125 ?-1200. At $,642-600. At $,5?-480.

A. $16200. 3. What is the product of 2s. 6 d. multiplied by 2?-5. By 4?-10. By 7?-17-6. By 10 ?-1-5. By 12 ?-1-10.

A. 4£. 7 s. 6 d.

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

A. 3£. 13 s. 34 d. 5. Reduce }, 4, and }, to the least common denominator.

.1. 16, 18, 6. Change 2000 francs to federal money. A. $375. 7. Teo+,3+ Theo +673 + Tooso. A. 673,37505.

8. 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 3 months 15 days ?-371. For 11 month ?-159. For 10 days ?-35 For 5 days ?-17. For 4 days ?-14. A. $1,232 +:

10. What is the amount of $300, at 7 per cent., for 1 year ?321. At 3 per cent. 2-309. At 53 per cent. ?-31650. 'At 93 per cent. ?-32925. Al 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. 2-40602.

A. $705,602. 12. What is the compound interest of $360 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. 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; buty 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 PROPORTION.

I 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 one gallon will cost first. It is 25

low many

cents. Then, 3 gallons are 3 times 25,=75 cents. Proceed in the same manner 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? 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 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 ? will 60 cents? How many will 108 cents ?

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? 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 40000 ?

8. If you pay 16 cents for 4 oranges, how many cents will 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 8 cost? What will 25 cost? What will 30 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 many cents will buy 3? Will buy 4? 5? 6? 7 ? 8? 9? 10? 20? 30? 40 ?

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

cost? (If cost 4 dollars, ß will cost 2 dollars.) What will f? What ? What ?? What? What ij? What

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