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 ?

Ans. $215'103.

COMPOUND INTEREST.

T 91. A promises to pay B $256 in three years, with interest annually; but at the end of 1 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. ?

162816 compound interest, 2d year, added together. principal,

271'36

287'6416 amount or principal for 3d year.

'06

17'25846 compound interest, 3d year, added together. principal

287'641

do.

first principal subtracted.

compound interest for 3 years.

what the amount for 3 years?

2. At 6 per cent., what will be the compound interest, and what

the amount, of $1 for 2 years?

for 4 years?

for 5 years? for 8 years?

for 7 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.

Note 1. Four decimals in the above numbers will be sufficiently 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 $600'50 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, 2'65329 X 600'50 $1593'30+Ans. at 5 per cent.; and 3'20713 X 600′50 = $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 3 years and 4 months?

for 12 years?
6 months and 18 days?

for 24 years 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 premium for insurance, commission, &c.,-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.

II. When there are months and days in the given time, to find the interest on any sum of money at 6 per cent.,-Multiply 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 to consider that 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 1 for every 6 days.

IV. If the sum giren be in pounds, shillings, pence and farthings, -Reduce the shillings, &c. to the decimal of a pound, by inspection, (76) then proceed in all respects as in federal money. Having found the interest, the decimal part, by reversing the operation, may be reduced back to shillings, pence and farthings.

V. If the interest 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 $2'29, 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.

2 days?

6. What is the interest of $200 for 1 day? 3 days? 4 days? 5 days? Ans. for 5 days, $0'166. 7. What is the interest of half a mill for 567 years?

Ans. $0'017.

per

8. What is the interest of $81, for 2 years 14 days, at

cent. ?

per cent.?

cent. ?

3 per cent.?

cent. ?

6 per cent.?

cent.?

8 per cent.?

cent.?

12 per cent.?

per cent.?

4 per cent.?

7 per cent.?

9 per cent.?

12 per cent.?

2 per 5 per

7 per

10 per

Ans. to last, $20'643,

9. What is the interest of 9 cents for 45 years 7 months 11 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. Ans. $207'22.

11. B's note of $56'75 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. $328 32. 13. Supposing a note of $317'92, dated July 5, 1797, on which were endorsed the following payments, viz. Sept. 13, 1799, $208'04; March 10, 1800, $76; what was there due Jan. 1, 1801?

Ans. $83'991.

SUPPLEMENT TO INTEREST.

QUESTIONS.

1. What is interest? 2. How is it computed? 3. What is understood by rate per cent. ? 4. amount?

8.

11.

13.

6.

by

by principal? 5.

by commission?

premium? 10.

by legal interest? 7. insurance? 9. policy? stock? 12. What is understood by stock being at par? above par? 14. below par? 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. 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. $50 652. 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 ? Ans. $174'53.

4. E's note of $870'05 was given Nov. 17, 1800, on interest after 90 days; Feb. 11, 1805, he paid $186'06; what was there due Dec. 23, 1807 ? Ans. $1045'34.

5. What will be the annual insurance, at § 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 1 per cent.? cent.?

at

at per cent.?

Note. Consult T 82, ex. 11.

at 7

per cent.?
at

per cent.?

Ans. at

16 per

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 $560'75 of stock, at 93 per cent.?

Ans. $521'497. 10. What principal at 7 per cent. will, in 9 months 18 days, amount to $422'40 ? 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 them again for $300, payable in 9 months; what did he gain, discounting at 6 per cent.? Ans. $37'081.

13. Sold 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. What 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.?

17. If I buy candles at $167 per lb., and sell them at 20 cents, what shall I gain in laying out $100?

Ans. $19'76. 18. Bought hats at 4 s. apiece, and sold them again at 4 s. 9 d.;

what is the profit in laying out 100£.?

19. Bought 37 gallons of brandy, at $1'10 per for $40; what was gained or lost per cent.?

Ans. 18 £. 15 s. gallon, and sold it

20. At 4 s. 6 d. profit on £., how much is gained in laying out 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 per cent.?

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. proving so good as how must I sell it Ans. 12 s. 4 d. 24. Bought 50 gallons of brandy, at 92 cents per gallon, but by accident 10 gallons leaked out; at what rate must I sell the remain

23. Bought cloth at 15 s. per yard, which not I expected, I am content to lose 17 per cent.; per yard?