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The commission, for the purchase or sale of goods in the
city of New York, varies from 2J to 12 J per cent, and under
some circumstances even higher rates are paid.

Brokerage is an allowance made to an agent who buys or
sells stocks, uncurrent money, or bills of exchange, and is
generally reckoned at so much per cent on the par value of
the stock. The brokerage, in the city of New York, is gene-
rally one-fourth per cent on the par value of the stock.

EXAMPLES.

1. What is the commission on $4396 at per 6 cent?

OPERATION.

NOTE. We here find the commission, as $4396

in simple percentage, by multiplying by the de- Q g

cimal which expresses the rate per cent. :

Am. $263.76.

2. A factor sells 60 bales of cotton at $425 per bale, and
is to receive 2 J per cent commission : how much must he pay
over to his principal ?

3. A drover agrees to purchase a drove of cattle and to sell
them in New York city for 5 per cent on what he may re-
ceive ; he expends in the purchase $4250, and sells them at
an advance of 10 per cent : how much is his commission ?

4. A commission merchant sells goods to the amount of
$8750, on which he is to be allowed 2 per cent, but in con-
sideration of paying the money over before it is due, he is to
receive !- per cent additional : how much must he pay over
to his principal ?

5. A broken bank has a circulation of $98000 and pur-
chases the bills a,t 85 per cent : how much is made by the
operation ?

248. What is commission ? What is brokerage ?



236 PERCENTAGE.

6. Merchant A sent to B, a broker, $3825 to be invested in
stock ; B is to receive 2 per cent on the amount paid for the
stock : what was the value of the stock purchased ?

OPERATION.

ANALYSTS. Since the broker re- 1 .02)3825 .00($3750vl?is.

ceives 2 per cent, it will require 306

$1.02 to purchase 1 dollar's worth

of stock; hence, there will be as 765

many dollar's worth purchased as 714
$1.02 is contained times in $3825 ;
that is, $3750 worth.

510

7. Mr. Jones sends his broker $18560 to be invested in
U. S. Stocks, which are 15 per cent above par ; the broker is
to receive one per cent ; how many shares of $100 each can
be purchased ?

ANALYSIS. Since the premium is 15
per cent, and the brokerage 1 per cent, OPERATION.

each dollar of par value will cost $1 1.16)18560
plus the premium, plus the brokerage^

$1.16 : hence, the amount purchased ' quotient,

wiU be as many dollars as $1.16 is or, 160 shares,
contained times in $18560.

8. I have $4999.89 to be laid out in stocks, which are 15
per cent below par : allowing 2 per cent commission, how
much can be purchased at the par value ?

ANALYSIS. Since the stock is at a dis-
count of 15 per cent, the market value will OPERATION.
be 85 per cent ; add 2 per cent, the broker- . 87)4999.89
age, gives 87 per cent=.87. The amount v-^ . ^ .

purchased will be as many dollars as .87 is
contained times in $4999,89.

Hence, to find the amount at par value,

Divide the amount to be expended by the market value of
$1 plus the brokerage ; and the quotient ivill be the amount
in par value.

9. Messrs. Sherman & Co. received of Mr Gilbert $28638.50
to be invested in bank stocks, which are 12i per cent above
par, for which they are to receive one-fourth of one per cent
commission : how many shares of $127 each can they buy ?



LOSS OR GAIN. 237

10. The par value of Illinois Railroad stock is 100. It
sells in market at 72 J : if I pay J per cent brokerage, how
many shares can I buy for $5820 ?

PROFIT AND LOSS.

249. Profit or loss is a process by which merchants dis-
cover the amount gained or lost in the purchase and sale of
goods. It also instructs them how much to increase or
diminish the price of their goods, so as to make or lose so
much per cent.

EXAMPLES.

1. Bought a piece of cloth containing 75?/d. at $5.25 per
yard, and sold it at $5.75 per yard : how much was gained
in the trade ?

OPERATION.

ANALYSIS. We first find tho $5.75 p r i ce of 1 yard,
profit on a single yard, and then AC op; oc .^ n f i vnrf i
multiply by the number of yards, !^_ co
which is *5. 50cfe. profit on 1 yard :

then, $0.50x75=$37.50.

2. Bought a piece of calico containing 56 yards, at 27 cents
a yard : what must it be sold for per yard to gain $2.24 ?

OPERATION.

56 yards at 27 cents=$15.12

ANALYSIS. First find the Profit - 2.24

cost, then add the profit and T , ,, ,,

divide the sum by the number Ifc must sel1 f r ' WM.
of yards 56)17,36

31 cts. a yard.

250. Knowing the per cent, of gain or loss and the
amount received, to find the cost.

1. I sold a parcel of goods for $195.50, on which I made
15 per cent : what did they cost me ?

ANALYSIS. 1 dollar of the cost plus 15 per OPERATION.

cent, will be what that which cost $1 sold for, 1.15) 195.50

viz , $1.15 : hence, there will be as many ^ K

dollars of cost, as $1.15 is contained times in * L1() Ans -
what the goods brought.

349. What is loss or gain ?



238 PERCENTAGE.

2. If I sell a parcel of goods for $170, by which I lose
15 per cent, what did they cost ?

ANALYSIS. 1 dollar of the cost less 15 per OPERATION.
cent, will be what that which cost 1 dollar sold .85) 170
for, viz., $0.85 : hence, there will be as many
dollars of cost, as .85 is contained times in
what the goods brought.

Hence, to find the cost,

Divide the amount received by 1 plus the per cent ivhen
there is a gain, and by 1 minus the per cent when there
is a loss, and the quotient will be the cost.

EXAMPLES.

1. Bought a piece of cassimere containing 28 yards at
1 dollars a yard ; but finding it damaged, am willing to sell
it at a loss of 15 per cent : how much must be asked per
yard?

2. Bought a hogshead of brandy at $1.25 per gallon, and
sold it for $78 : was there a loss or gain ?

3. A merchant purchased 3275 bushels of wheat for which
he paid $3517.10, but finding it damaged, is willing to lose
10 per cent : what must it sell for per bushel ?

4. Bought a quantity of wine at $1.25 per gallon, but it
proves to be bad and am obliged to sell it at 20 per cent less
than I gave : how much must I sell it for per gallon ?

5. A farmer sells 125 bushels of corn for 75 cents per
bushel ; the purchaser sells it at an advance of 20 per cent :
how much did he receive for the corn ?

6. A merchant buys 1 tun of wine for which he pays $725,
and wishes to sell it by the hogshead at an advance of 15 per
cent : what must be charged per hogshead ?

7. A merchant buys 158 yards of calico for which he pays
20 cents per yard ; one-half is so damaged that he is obliged
to sell it at a loss of 6 per cent : the remainder he sells at an
advance of 19 per cent : how much did he gain?

8. If I buy coffee at 16 cents and sell it at 20 cents a
pound, how much do I make per cent on the money paid ?

250. Knowing the per cent of gain or loss and the amount received
how do you find the cost ?



INSURANCE. i!39

9. A man bought a house and lot for $1850.50, and sold it
for $1517.41 : how much per cent did he lose ?

10. A merchant bought 650 pounds of cheese at 10 cents
per pound, and sold it at 12 cents per pound : how much did
he gain on the whole, and how much per cent on the money
laid out ?

11. Bought cloth at $1.25 per yard, which proving bad, I
wish to sell it at a loss of 18 per cent : how much must I
ask per yard ?

12. Bought 50 gallons of molasses at 75 cents a gallon,
10 gallons of which leaked out. At what price per gallon
must the remainder be sold that I may clear 10 per cent on
the cost ?

13. Bought 67 yards of cloth for $112, but 19 yards being
spoiled, I am willing to lose 5 per cent : how much must I
sell it for per yard ?

14. Bought 67 yards of cloth for $112, but a number of
yards being spoiled, I sell the remainder at $2.216| per yard,
and lose 5 per cent : how many yards were spoiled ?

15. Bought 2000 bushels of wheat at $1.75 a bushel, from
which was manufactured 475 barrels of flour : what must
the flour sell for per barrel to gain 25 per cent on the cost of
the wheat ?

INSURANCE.

251. INSURANCE is an agreement, generally in writing, by
which an individual or company bind themselves to exempt
the owners of certain property, such as ships, goods, houses,
&c., from loss or hazard.

The POLICY is the written agreement made by the parties.

PREMIUM is the amount paid by him who owns the property
to those who insure it, as a compensation for their risk. The
premium is generally so much per cent on the property in-
sured.

EXAMPLES.

1. What would be the premium for the insurance of a
house valued at $8754 against loss by fire for one year, at
\ per cent ?

251. What is insurance? What is the policy? What is the pre-
mium ? How is it reckoned ?



PERCENTAGE.

2. What would bo the premium for insuring a ship and
cargo, valued at $37500, from New York to Liverpool, at 3
per cent ?

3. What would be the insurance on a ship valued at
$47520 at J per cent ; also at J per cent?

4. What would be the insurance on a house valued at
$14000 at 1J per cent?

5. What is the insurance on a store and goods valued at
$27000, at 2 J per cent ?

6. What is the premium of insurance on $9870 at 14 per
cent?

7. A merchant wishes to insure on a vessel and cargo at
sea, valued at $28800 : what will be th^ premium at 1| per
cent ?

8. A merchant owns three-fourths of a ship valued at
$24000, and insures his interest at 2| per cent : what does
he pay for his policy ?

9. A merchant learns that his vessel and cargo, valued
at $36000, have been injured to the amount of $12000 ; he
effects an insurance on the remainder at 5| per cent ; what
premium does he pay ?

10. My furniture, worth $3440, is insured at 2f per cent ;
my house, worth $1000, at 1 J per cent ; and my barn, horses
and carriages, worth $1500, at 3J per cent : what is the
whole amount of my insurance ?

11. A man bought a house, and paid the insurance at 2|
per cent, the whole of which amounted to $1845 : what was
the value of the house and the amount of the insurance ?

12. What would it cost to insure a store, worth $3240, at
f per cent, and the stock, worth $7515.75, at f per cent?

13. A merchant imported 250 pieces of broadcloth, each
piece containing 36| yards, at $3.25 cents a yard. He paid
4| per cent insurance on the selling price, $4.50 a yard. If
the goods were destroyed by fire, and he got the amount of
insurance, how much did he make ?

14. A vessel and cargo, worth $65000, are damaged to the
amount of 20 per cent, and there is an insurance of 50 per
cent on the loss: how much insurance will the owner re-
ceive ?



INTEREST. 241



INTEREST.

252. INTEREST is an allowance made for the use of money
that is borrowed.

PRINCIPAL is the money on which interest is paid.
AMOUNT is the sum of the Principal and Interest.
For example : If I borrow 1 dollar of Mr. Wilson for 1
year, and pay him 7 cents for the use of it ; then,

1 dollar is the principal,

7 cents is the interest, and

$1.07 the amount.

The RATE of interest is the number of cents paid for the
use of 1 dollar for 1 year. Thus, in the above example, th*e
rate is 7 per cent per annum.

NoTE.-VThe term per cent means, ty the hundred; and per
annum means by the year. As interest is always reckoned by the
year, the term per annum is understood and omitted.

CASE I.

253. To find the interest of any principal for one or more
years.

1. What is the interest of $1960 for 4 years, at 7 per
cent?

ANALYSIS. The rate of interest

being 7 per cent, is expressed deci- OPERATION.

mallyby.07: hence, each dollar, in $1960

1 year will produce .07 of itself, and A 7 rq fp

$1960 will produce .07 of $1960,

or $137.20. Therefore, $137.20 is the 137.20 int. for It/r.

interest for 1 year, and this interest 4 No. of years,

multiplied by 4, gives the interest for AC 4 Q Qft

4 years : hence, the following $D48.U

RULE. Multiply the principal by the rate, expressed
decimally, and the product by the number of years.

252. What is interest? What is principal? What is amount?
What is rate of interest ? \Vhat does per annum mean ?

253. How do you find the interest of any principal for any number of
years ? Give the analysis.



242 SIMPLE INTEREST.

EXAMPLES.

1. What is the interest of $365.874 for one year, at 5J
per cent ?

OPERATION.

365.874

ANALYSIS. We first find the in- 951

terest at ^ per cent, and then the -
interest at 5 per cent ; the sum is 1.82937 per cent,

the interest at 5 per cent. 18.29370 5 per cent.

Ans. $20.12307 5J per cent.

2. What is the interest of $650 for one year, at 6 per cent ?

3. What is the interest of $950 for 4 years, at 7 per cent ?

4. What is the amount of $3675 in 3 years, at 7 per cent ?

5. What is the amount of $459 in 5 years, at 8 per cent ?

6. What is the amount of $375 in 2 years, at 7 per cent?

7. What is the interest of $21 1.26 for 1 year, at 4J per ct. ?

8. What is the interest of $1576.91 for 3 years, at 7 per ct. ?

9. What is the amount of $957.08 in 6 years, at 3J per ct. ?

10. What is the interest of $375.45 for 7 years, at 7 per ct. ?

11. What is the amount of $4049.87 in 2 years, at 5 per ct. ?

12. What is the amount of $16199.48 in 16 yrs., at 5J per ct. ?

NOTE. When there are years and months, and the months are
aliquot parts of a year, multiply the interest for 1 year by the years
and months reduced to the fraction of a year.

EXAMPLES.

1. What is the interest of $326.50, for 4 years and

2 months, at 7 per cent ?

2. What is the interest of $437.21, for 9 years and

3 months, at 3 per cent ?

3. What is the amount of $1119.48, after 2 years and
6 months, at 7 per cent ?

4. What is the amount of $179.25, after 3 years and

4 months, at 7 per cent?

5. What is the amount of $1046.24, after 4 years and
3 months at 5^ per cent ?



SIMPLE INTEREST. 24:3



CASE II.

254. To find the interest on a given principal for any rate
and time.

1. What is the interest of $876.48 at 6 per cent, for
4 years 9 months and 14 days ?

ANALYSIS. The interest for 1 year is the product of the princi-
pal multiplied by the rate If the interest for 1 year be divided
by 12, the quotient will be the interest for 1 month : if the interest
for 1 month be divided by 30, the quotient will be the interest
for 1 day.

The interest for 4 years is 4 times the interest for 1 year ; the
interest for 9 months, 9 times the interest for 1 month ; and the
interest for 14 days, 14 times the interest for 1 day

OPERATION.

$876.48
.06



12)52.5888=int. for lyr. 52.5888 x 4 =$210.3552 4yr.
30)4.3824 =int. for Imo. 4.3824 x 9 = $ 39.4416 9mo.
.14608=int. for Ida. .14608 x 14=$ 2.0451 Udg.
Total interest, $251.84194-

Hence, we have the following

RULE. I. Find the interest for 1 year :

II. Divide this interest by 12, and the quotient will be the
interest for 1 month :

III. Divide the interest for 1 month by 30, and the quo-
tient will be the interest for 1 day.

IY. Multiply the interest for 1 year by the number of
years, the interest for 1 month by the number of months, and
the interest for 1 day by the number of days, and the sum
of the product will be the required interest.

NOTE. In computing interest the month is reckoned at 30 days.

2. What is the interest of $132.26 for 1 year 4 months
and 10 days, at 6 per cent per annum ?

3 What is the interest of $25.50 for 1 year 9 months and
12 days, at 6 per cent ?

254. How do you find the interest for any time at any rate ?



244: SIMPLE INTEREST.

^ 2D METHOD.

255. There is another rule resulting from the last analysis,
which is regarded as the best general method of computing
interest.

RULE. I. Find the interest for 1 year and divide it bylZ:
the quotient will be the interest for 1 month.

II. Multiply the interest for 1 month by the time expressed
in months and parts of a month, and the product will be the
required interest.

NOTE, Since a month is reckoned at 30 days, any number of
days is reduced to decimals of a month by dividing the days by 3.

EXAMPLES.

1. What is the interest of $327.50 for 3 years 7 months
and 13 days, at 7 per cent ?

OPERATION.

3yrs.=3Qmos. $327.50

7mos. .07

13 days A\mos. 12)22.9250 =int. for 1 year.

Timer=43.4jwos. 1.9104 + =int. for 1 month.

NOTE. The method em- 43.4^ =time in months,

ployed, and the number of 6368
decimal places used, in com-
puting interest, may affect
the mills, and possibly, the

last figure in cents. It is best 7 64 1 6

to use 4 places of decimals. $32.97504 Ans.

2. What is the interest of $1728.60, at 7 per cent, for

2 years 6 months and 21 days ?

3. What is the interest of $288.30, at 7 per cent, for

I year 8 months and 27 days ?

4. What is the interest of $576.60, at 6 per cent, for
10 months aucl 18 days?

5. What is the interest of $854.42, at 6 per cent, for

3 months and 9 days ?

6. What is the interest of $1153.20, at 6 per cent, for

I 1 months and 6 days ?

255. How do you find the interest for years, months and days by the
second method ?



SIMPLE INTEREST. 245

7. What is the interest of $2306.54, at 5 per ceut, for
7 months and 28 days ?

8. What is the interest of $4272.10, at 5 per cent, for
10 months and 28 days?

9. What is the interest of $1620, at 4 per cent, for 5 years
and 24 days ?

10. What is the interest of $2430.72, at 4 per cent, for
10 years and 4 months ?

11. What is the interest of $3689.45, at 7 per cent, for
4 years and 7 months ?

12. What is the interest 01 $2945.96, at 7 per cent, for
7 years and 3 days ?

13. W T hat is the interest, at 8 per cent, of $675.89, for
3 years 6 months and 6 days ?

14. What is the interest, at 8 per cent, on $12324, for

3 years and 4 months ?

15. What is the interest, at 9 per cent, on $15328.20, for

4 years and 7 months ?

16. What is the interest of $69450 for 1 year 2 months
and 12 days, at 9 per cent ?

17. What is the interest of $216.984 for 3 years 5 months
and 15 days, at 10 per cent ?

18. What is the interest of $648.54 for 7 years 6 months,
at 4J per cent ?

19. What is the interest of $1297.10 for 8 years 5 months,
at 5 1 per cent ?

20. What is the interest of $864.768 for 9 months 25 days,
at 6 \ per cent ?

21. What is the interest of $2594.20 for 10 months and 9
days, at 7 1 per cent?

22. What is the amount of $2376.84 for 3 years 9 months
and 12 days, at 8 J per ceut ?

23. What is the amount of $5148.40 for 7 years 11 months
and 23 days, at 9 J per cent ?

24. What is the amount of $3565.20 for 3 years 9 months,
at 10 J per cent?



24:6 SIMPLE INTEREST.

25. What is the amount of $125.75 for 1 year 9 months
and 27 days, at 7 per cent ?

26. What is the amount of $256 for 10 months 15 days, at
7 J per cent ?

27. What is the interest on a note of $264.42, given Janu-
ary 1st, 1852, and due Oct. 10th, 1855, at 4 per cent?

28. Gave a note of $793.26 April 6th, 1850, on interest at
7 per cent : what is due September 10th, 1852 ?

29. What amount is due on a note of hand given June 7th,
1850, for $512.50, at 6 per cent, to be paid Jan. 1st, 1851 ?

30. What is the interest on $1250.75 for 90 days, at 10
per cent ?

31. What is the amount of $71.09 from Feb. 8th, 1848, to
Dec. 7th, 1852, at 6 j per cent ?

32. What will be due on a note of $213.27 on interest
after 90 days, at 7 per cent, given May 19th, 1836, and pay-
able October 16th, 1838 ?

33. What is the interest of $426.54, from August 15th,

1837, to March 13th, 1840, at 7 per cent?

34. What is the interest of $2132.70, from Nov. 17th,

1838, to Feb. 2d, 1839, at 7J per cent?

35. What is the interest of $38463, from April 27th, 1815,
to Sept. 2d, 1824, at 8 per cent ?

36. What is the interest of $14231.50, from June 29th,
1840, to April 30th, 1845, at 8J per cent?

37. What is the interest of $426.50, from Sept. 4th, 1843,
to May 4, 1849, at 9 per cent?

38. What is the interest of $4320, from Dec. 1st, 1817, to
Jan. 22d, 1833, at 9J per cent?"

39. What is the amount of $397.16, from March 24, 1824,
to March 31st, 1835, at 10| per cent ?

40. What is the amount of $328.12, from July 4th, 1809,
to Feb. 15th, 1815, at 3 per cent ?

41. What is the amount of $164.60, from Sept. 27th, 1845,
to March 24, 1855, at 1J per cent?

42. What is the amount of $1627.50, from July 4th, 1839,
to August 1st, 1855, at 8 per cent?



PARTIAL PAYMENTS. 24:7



CASE III.

256. When the principal is in pounds, shillings and
pence.

1. What is the interest, at 7 per cent, of 27 15s. 9d.,
for 2 years ?

OPERATION.

ANALYSIS. The interest on pounds 27 15s. 9J. = 27.7875

and decimals of a pound is found in Q>J
the same way as the interest on dol-

lars and decimals of a dollar: after 1.945125

which the decimal part of the interest 2
may be reduced to shillings and



Ans. 3 178.

1. Reduce the shillings and pence to the decimal of a
pound and annex the result to the pounds.

II. Find the interest as though the sum were United
States Money, after which reduce the decimal part to shil-
lings and pence.

2. What is the interest of 67 19s. Qd. } at 6 per cent, for
3 years 8 months 16 days ?

3. What is the interest of 127 15s. 4d., at 6 per cent,
for 3 years and 3 months ?

4. What is the interest of 107 16s. IQd., at 7 per cent,
for 3 years 6 months and 6 days ?

5. What will 279 13s. 8d. amount to in 3 years and a
half, at 5J per cent per annum?

PARTIAL PAYMENTS.

257.. A PARTIAL PAYMENT is a payment of a part of a note
or bond.

We shall give the rule established in New York (see
Johnson's Chancery Reports, vol. I. page 17), for computing
the interest on a bond or note, when partial payments have
been made. The same rule is also adopted in Massachusetts,
and in most of the other states.

256. How do you find the interest when the principal is in pounds,
shillings and pence ?



248 PARTIAL PAYMENTS.

RULE. I. Compute the interest on the principal to the
time of the first payment, and if the payment exceed this
interest, add the interest to the principal and from the sum
subtract the payment : the remainder forms a new principal :

II. But if the payment is less than the interest, take no
notice of it until other payments are made, which in all,
shall exceed the interest computed to the time of the last
payment : then add the interest, so computed, to the princi-
pal, and from the sum subtract the sum of the payments :
the remainder will form a new principal on which interest
is to be computed as before.

NOTE In computing interest on notes, observe that the day on
which a note is dated and the day on which it falls due, are not
both reckoned in determining the time, but one of them is always
excluded. Thus, a note dated on the first day of May and falling
due on the 16th of June, will bear interest but one month and
1 5 days.

EXAMPLES.



$349.998 Buffalo, May 1st, 1826.

1. For value received, I promise to pay James Wilson or
order, three hundred and forty-nine dollars ninety-nine cents
and eights mills with interest at 6 per cent.

James Pay well.

On this note were endorsed the following payments :
Dec. 25th, 1826 Received $49.998
July 10th, 1827 " $ 4.998
Sept. 1st, 1828 " $15.008
June 14th, 1829 " $99.999
What was due April 15th, 1830 ?

Principal on int. from May 1st, 1826, - - - - $349.998
Interest to Dec. 25th, 1826, time of first pay-
ment, 7 months 24 days 13.649 +

Amount, - - - $363.647



257. What is a partial payment? What is the rule for computing
Interests when there are partial payments ?



PARTIAL PAYMENTS. 249

Payment Dec. 25th, exceeding interest then due $ 49.998

Remainder for a new principal $313.649

Interest of $313.649 from Dec. 25, 1826, to

June 14th, 1829, 2 years 5 months 19 days, - $ 46.4721

Amount "$360.1211

Payment, July 10th, 1827, .less than {* ^ QQO

interest then due ) * '

Payment, Sept. 1st, 1828 15.008

Their sum less than interest then due - $20.006
Payment, June 14th, 1829 - - - - 99.999
Their sum exceeds the interest then due- - - $120.005

Remainder for a new principal, June 14, 1829, $240.1161
Interest of $240.168 from June 14th, 1829, to

April 15th, 1830, 10 months 1 day - - - $ 12.0458

Total due, April 15th, 1830 - -"$252.1619 +

$3469.327 New York, Feb, 6, 1825.

2. For value received, I promise to pay William Jenks, or
order, three thousand four hundred and sixty-nine dollars and
thirty-two cents, with interest from date, at 6 per cent.

Bill Spendthrift.

On this note were endorsed the following payments :
May 16th, 1828, received $ 545.76
May 16th, 1830, " $1276.00
Feb. 1st, 1831, " $2074.72

What remained due Aug llth, 1832 ?

3. A's note of $635.84 was dated September 5, 1817, on
which were endorsed the following payments, viz. : Nov.


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Online LibraryCharles DaviesSchool arithmetic. Analytical and practical → online text (page 17 of 24)