5. A merchant bought a quantity of tea for $365, which, proving to have been damaged, he sold for $332'15; what did he lose per cent. ? Ans. 9 per cent,

6. If I buy cloth at $2 per yard, and sell it for $2'50 per yard, what should I gain in laying out $100?

Ans. $25. 7. Bought indigo at $1'20 per lb., and sold the same at 90 cents per lb.; what was lost per cent.?

Ans. 25 per cent.

8. Bought 30 hogsheads of molasses, at $600; paid in duties $20'66; for freight, $40'78; for porterage, $6'05, and for insurance, $30'84: if I sell them at $26 per hogshead, how much shall I gain per cent.? Ans. 11'695 per cent.

The principal, rate per cent., and interest being given, to find the time.

TT 89. 1. The interest on a note of $36, at 7 per cent., was $378; what was the time?

The interest on $36, 1 year, at 7 per cent., is $2'52; hence, $378 $2'52 1'5 years, the time required; that is,-Find the interest for 1 year on the principal given, at the given rate, by which divide the given interest; the quotient will be the time required, in years and decimal parts of a year; the latter may then be reduced to months and days.

Ans. 1 year 6 months. 2. If $3171 interest be paid on a note of $226′50, what was the time, the rate being 6 per cent.?

Ans. 2'33

2 years 4 months. 3. On a note of $600, paid interest $20, at 8 8 per cent.; what was the time?

Ans. 416 +: 5 months so nearly as to be called 5, and would be exactly 5 but for the fraction lost.

4. The interest on a note of $217'25, at 4 per cent., was $28'242; what was the time? Ans. 3 years 3 months.

Note. When the rate is 6 per cent., we may divide the interest by the principal, removing the separatrix two places to the left, and the quotient will be the answer in months.

To find the interest due on notes, &c. when partial payments

have been made.

T 90. In Massachusetts the law provides, that payments shall be applied to keep down the interest, and that neither interest nor payment shall ever draw interest. Hence, if the payment at any time exceed the interest computed to the same time, that excess is taken from the principal; but if the payment be less than the interest, the principal remains unaltered: Wherefore, we have this RULE :-Compute the interest to the first time when a payment was made, which, either alone, or together with the preceding payments, if any, exceeds the interest then due; add that interest to the principal, and from the sum subtract the payment, or the sum of the payments, made within the time for which the interest was computed, and the remainder will be a new principal, with which proceed as with the first.

1. For value received, I promise to pay JAMES CONANT, OF order, one hundred sixteen dollars sixty-six cents and six mills, with interest. May 1, 1822.

$116,666.

SAMUEL ROOD.

On this note were the following endorsements:

Dec. 25, 1822, received $16'666

Note. In finding the

times for computing the

June 14, 1825,

$33'333

interest, consult TT 40.

April 15, 1826,

$62'000

What was due August 3, 1827?

Ans. $23775

The first principal on interest from May 1, 1822, $116'666 Interest to Dec. 25, 1822, time of the first pay

ment, (7 months 24 days,)

4'549

Amount, $121'215

Payment, Dec. 25, exceeding interest then due,

16'666

Remainder for a new principal,

104'549

Interest from Dec. 25, 1822, to June 14, 1825,

(29 months 19 days,)

·

15'490

Amount carried forward,

120'039

Amount brought forward, $120'039

Payment, July 10, 1823, less than interest

then due,

Payment, Sept. 1, 1824, less than interest

then due,

Payment, June 14, 1825, exceeding interest then due,

$1'666

5'000

33'333

Remainder for a new principal, (June 14, 1825,) Interest from June 14, 1825, to April 15, 1826, (10 months 1 day,)

$39'999

80'040

4'015

Amount, $ 84'055

62'000 $22'055

Payment, April 15, 1825, exceeding interest then due,

Remainder for a new principal, (April 15, 1826,) Interest due Aug. 3, 1827, from April 15, 1826, (15 months 18 days,)

Balance due Aug 3, 1827,

16720

$23'775

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 3 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

P

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.

'06

15'36 interest,

256'00 principal, to be added together.

271'36 amount, or principal for 2d year.
'06

16'2816 compound interest, 2d year, added to-
271'36 principal,
do. Sgether.

287'6416 amount, or principal for 3d year.

'06

17'25846 compound interest, 3d year, added to

287 641

principal,

304'899 256

amount.

Ans. $48'899

do.

first principal subtracted.

}

Sgether.

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?

for 3 years?

what the amount

for 5 years?

for

for 8 years?

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 for 3 years and 4 months?

years?

?

for 12 years
for 24 years, 6 months, and 18 days?

Ans. to las, $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