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2. For value received, I promise to pay JAMES LOWELL, or order, eight hundred sixty-seven dollars and thirty-three cents, with interest. Jan. 6, 1820. $867'33.
HIRAM SIMSON. On this note were the following endorsements, viz. April 16, 1823, received $136'44. April 16, 1825, received $319. Jan. 1, 1826, received $518-68. What remained due July 11, 1827 ?
9 91. A promises to pay B $256 in three years, with interest annually ; but at the end of i year, not finding it convenient to pay the interest, he consents to pay interest on the interest from that time, the same as on the principal.
Note. Simple interest is that which is allowed for the principal only; compound interest is that which is allowed for both principal and interest, when the latter is not paid at the time it becomes due.
Compound interest is calculated by adding the interest to the principal at the end of each year, and making the amount the principal for the next succeeding year.
1. What is the compound interest of $256, for 3 years, at 6 per cent. ?
$256 given sum, or first principal.
15-36 interest,, } to be added together.
17425846 compound interest, 3d year, } added together.
first principal subtracted. Ans, $486899 compound interest for 3 years. 2. At 6 per cent., what will be the compound interest, and what the amount, of $1 for 2 years ? what the amount for 3 years ?
for 4 years?
for 6 years?
Ans, to the last, $1'593 +. It is plain that the amount of $2, for any given time, will be 2 times as much as the amount of $1; the amount of $3 will be 3 times as much, &c.
Hence, we may form the amounts of 1 for several years into a table of multipliers for finding the amount of any sum for the same time.
TABLE, Showing the amount of $1 or 1 £., &c. for any number of years, not exceeding 24, at the rates of 5 and 6 per cent. compound interest. Years.). 5 per cent 6 per cent.
5 per cent.
6 per cent.
13 1-88564 +2'13292
16 2'18287 2'54035 1'27 628 1'33822
17 2'29201 +2'69277 1'34009 + 1'41851
2'40661 + 2'85433 7 1'40710 1'50363
19 2'52695 3:02559 8 1'47745 1'59384
2'65329 +13'20713 1'55132 1'68947
21 2'78596 +3'39956 10 1'62889 1'79084
22 2'92526 +3•60353 11 1'71033 1'89829
23 3'07152 3'81974 12
11679585 +2'01219 + 24 13622509 14'04893 Note 1. Four decimals above numbers will be sufficient. ly accurate for most operations.
Note 2. When there are months and days, you may first find the amount for the years, and on that amount cast the interest for the months and days; this, added to the amount, will give the answer.
3. What is the amount of $600ʻ50 for 20 years, at 5 per cent. compound interest ?
at 6 per cent. ? $1 at 5 per cent., by the table, is $2'65329; therefore, 265329 X 600ʻ50 $1593'30' + Ans. at 5 per cent.; and 3-20713
X 600ʻ50 $1925'881 + Ans. at 6 per cent.
4. What is the amount of $40-20 at 6 per cent. compound interest, for 4 years? for 10 years ?
for 18 years? for 12 years? for 3 years and 4 months ? 6 months and 18 days?
Ans. to last, $168-137. Note. Any sum at compound interest will double itself in 11 years 10 months and 22 days.
From what has now been advanced, we deduce the following general
RULE. I. To find the interest when the time is 1 year, or, to find the rate per cent. on any sum of money, without respect to time, as the premia um for insurance, commişsion, foc., -Multiply the principal, or given sum, by the rate per cent., written as a decimal fraction; the product, remembering to point off as many places for decimals as there are decimals in both the factors, will be the interest, &c. required.
for 24 years
II. When there are months and days in the given time, to find the interest on unt; sum of money at 6 per cent., --Alultiply the principal by the interest on $1 for the given time, found by inspection, and the product, as before, will be the interest required."
III. To find the interest on $1 at 6 per cent., for any given time, by inspection,-It is only consider ihat the cents will be equal to half the greatest even number of the months; and the mills will be 5 for the odd month, (if there be one,) and i for every 6 days.
IV. If the sum giren be in pounds, shillings, pence and furthings, -Reduce the shillings, &c. to the decimal of a pound, by inspection, (976 :), then proceed in all respects as in fecitral money. Having found the interest, the decimal part, by reversing the operation, may be reduced back to shillings, pence and farthings.
V. If the irterest required be at any other rate than 6 per cent., (if there be months, or months and days, in the given time,)-First find the interest at 6 per cent.; then divide the interest so found by such part or parts, as the interest, at the rate required, exceeds or falls short of the interest at 6 per cent.; and the quotient, or quotients, added to or subtracted from the interest at 6 per cent., as the case may require, will give the interest at the rate required.
Note. The interest on any number of dollars, for 6 days, at 6 per cent., is readily found by cutting off the unit or right hand figure; those at the left hand will show the interest in cents for 6 days.
EXAMPLES FOR PRACTICE. 1. What is the interest of $1600 for 1 year and 3 months ?
Ans. $120. 2. What is the interest of $5'811, for 1 year 11 months ?
Ans. (668. 3. What is the interest of $229, for 1 month 19 days, at 3 per ct. ?
Ans. $'009. 4. What is the interest of $18, for 2 years 14 days, at 7 per cent. ?
Ans. $2'569. 5. What is the interest of $17'68, for 11 months 28 days?
Ans, $1'054. 6. What is the interest of $200 for 1 day? 2 days? 3 days?
4 days? 5 days? Ans. for 5 days, $0ʻ166. 7. What is the interest of half a mill for 567 years?
Ans. $0.017. 8. What is the interest of $81, for 2 years 14 days, at per 4 per cent.?
per cent. ? cent. ? 3 per cent. ?
43 per cent. ? cent. ? 6 7 per cent. ?
75 per -8 per cent. ?
9 per cent. ? cent. ? 12 per cent. ?
124 per cent. ?
Ans. to last, $20'643, 9. What is the interest of 9 cents for 45 years 7 months in days?
Ans. $0 246. 10. A's note of $175 was given Dec. 6, 1798, on which was endorsed one year's interest; what was there due Jan. 1, 1803 ?
Note. Consult ex. 16, Supplement to Subtraction of Compound Numbers.
2 per 5 per
per cent. ?
11. B's note of $5675 was given June 6, 1801, on interest after 90 days; what was there due Feb. 9, 1802 ?
Ans. $58'19. 12. C's note of $365'37 was given Dec. 3, 1797 ; June 7, 1800, he paid $97'16; what was there due Sept. 11, 1800 ? Ans. $323'32.
13. Supposing a note of $317'92, dated July 5, 1797, on which were endorsed the following payments, viz. Sept. 13, 1799, $208404 ; March 10, 1800, $76; what was there due Jan. 1, 1801 ?
SUPPLEMENT TO INTEREST.
QUESTIONS. 1. What is interest ? 2. How is it computed ? 3. What is anderstood by rate per cent. ?, 4. by principal ? 5. - by amount ? 6. by legal interest ? 7. by commission? 8.
insurance ? 9. premium ? 10. policy? 11.
stock? 12. What is understood by stock being at par? 13. above par ? 14.
15. The rate per cent. is a decimal carried to how many places ? 16. What are decimal expressions lower than hundredths ? 17. How is interest, (when the time is 1 year,) commission, insurance, or any thing else rated at so much per cent., without respect to time, found? 18. When the rate is 1 per cent., or less, how may the operation be contracted ? 19. How is the interest on $1, at 6 per cent. for any given time, found by inspection? 20. How is interest cast, at 6 per cent., when there are months and days in the given time? 21. When the given time is less than 6 days, how is the interest most readily found ? 22. If the sum given be in pounds, shillings, &c., how is interest cast? 23. When the rate is any other than 6 per cent., if there be months and days in the given time, how is the interest found ? 24. What is the rule for casting interest on notes, &c. when partial payments have been made, and what is the principle, on which the rule is founded ? 25. How may the principal be found, the time, rate per cent., and amount being given ?" 26. What is understood by discount ? 27. by present worth? 28. How is the principal found, the time, rate per cent., and interest being given? 29. How is the rate per cent. of gain or loss found, the prices at which goods are bought and sold being given? 30. How is the rate per cent. found, the principal, interest, and time being given ? 31. How is the time found, the principal, rate per cent., and interest being given ? 32. What is simple interest ? 33.
compound interest ? 34. How is compound interest computed ?
EXERCISES. 1. What is the interest of $273'51 for 1 year 10 days, at 7 per cent. ?
Ans. $19'677. 2. What is the interest of $486 for 1 year, 3 months, 19 days, at 8 per cent. ?
Ans. $50ʻ652. 3. D's note of $203'17 was given Oct. 5, 1808, on interest after three months ; Jan. 5 1809, he paid $50; what was there due May 2, 1811?
per cent. ?
4. E's note of $870'05 was given Nov. 17, 1800, on interest after 90 days; Feb. 11, 1905, he paid $186ʻ06; what was there due Dec. 23, 1807 ?
Ans. $1045-34. 5. What will be the annual insurance, at s per cent., on a house valued at $1600?
Ans, $10. 6. What will be the insurance of a ship and cargo, valued at $5643, at 1per cent. ? cent. ?
at 12 per cent. ? at 4 per cent. ? Note. Consult T 82, ex. 11. Ans. at & per cent. $42'322.
7. A man having compromised with his creditors at 62 cents on a dollar, what must he pay on a debt of $137'46 ? Ans. $85'912.
8. What is the value of $800 United States Bank stock, at 112} per cent. ?
Ans. $900. 9. What is the value of $56075 of stock, at 93 per cent. ?
Ans. $521'497. 10. What principal at 7 per cent. will, in 9 months 18 days, amount to $122'40'
Ans. $400. 11. What is the present worth of $426, payable in 4 years and 12 days, discounting at the rate of 5 per cent. ?
In large sums, to bring out the cents correctly, it will sometimes be necessary to extend the decimal in the divisor to five places.
Ans. $354'506. 12. A merchant purchased goods for $250 ready money, and sold then again for $300, payable in 9 months; what did he gain, discounting at 6 per cent. ?
Ans. $37'081. 13. Sok goods for $3120, to be paid, one half in 3 months, and the other half in 6 months; what must be discounted for present payment ?
Ans. $68'492. 14. The interest on a certain note, for 1 year 9 months, was $49'875; what was the principal ?
Ans. $475. 15. Wbat principal, at 5 per cent., in 16 months 24 days, will gain $35 ?
Ans. $500. 16. If I pay $15'52 interest for the use of $500 9 months and 9 days, what is the rate per cent. ?
i7. If I buy candles at $'167 per lb., and sell them at 20 cents, what shall I gain in laying out $100 ?
Ans. $1976. 18. Bought hats at 4 s. apiece, and sold them again at 4 s. 9 d.; what is the profit in laying out 100 £. ?
Ans. 18 £. 15 s. for $10; what was gained or lest new much is gained in laying out
19. Bought 37 gallons of brandy, at $1'10 per gallon, and sold it
20. At 4 s. 6 d. profit on 1 £., 100.£., that is, how much per cent. ?
Ans. 22 £. 10 s. 21. Bought cloth at $4:48 per yard; how must I sell it to gain 12
Ans. $5'04, 22. Bought a barrel of powder for 4 £.; for how much must it be sold to lose 10 per cent. ?
Ans. 3 £. 12 s. 23. Bought cloth at 15 s. per yard, which not proving so good as I expected, I am content to lose '174 per cent. ; how must sell it per yard?
Ans. 12 s. 41 d. 24. Bought 50 gallons of brandy, at 92 cents per gallon, but by accident 10 gallous leaked out; at what rate must I sell the remain
per cent. ?