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10)120(12 A's part.

2. A, B, and C, built a house which cost 500 dollars, of which A paid a certain sum; B paid 10 dollars more than FA, and C paid as much as A and B both ; how much did Fill each man pay?

Ans. A paid $120, B $130, and C $250. 3. A man bequeathed 1001. to three of his friends, after this manner; the first must have a certain portion, the second must have twice as much as the first, wanting 81. and the ihird must have three times as much as the first, wanting 15l. ; I demand how much each man must have ?

Ans. The first £20 10s. second £33, third £46 10s. 4. A labourer was hired for 60 days upon this condition ; that for every day he wrought he should receive 4s. and for every day he was idle should forfeit 2s. ; at the expiration of the time he received 71. 10s.; how many days did he work, and how many was he idle ?

Ans. He wrought 45 days, and was idle 15 days. 5. What number is that which being increased by its its , and 18 more, will be doubled ?

Ans. 72. 6. A man gave to his three sons all his estate in money, viz. to F half, wanting 501., to G one-third, and to H the 0, rest, which was 101. less than the share of G; I demand the sum given, and each man's part ?

Ans. the sum given was £360, whereof F had £130, G £120, and H £110.

7. Two men, A and B, lay out equal sums of money

in trade; A gains 1261. and B loses 871. and A's

money now double to B's; what did each lay out?

Ans. £300. 8. A farmer having driven his cattle to market, received for them all 1301. being paid for every ox 71. for every cow 51. and for every calf 11. 10s. there were twice as many cows as oxen, and three times as many calves as cows; how many were there of each sort?

Ans. 5 oxen, 10 cows, and 30 calves. 9. A, B, and C, playing at cards, staked 324 crowns; but disputing about tricks, each man took as many as he could; A got a certain number; B as many as A and 15 more; C got a 5th part of both their sums added together; how many did each get?

Ans. A got 127}, B 142}, C 54.

PERMUTATION OF QUANTITIES, IS the showing how many different ways any given num. ber of things may be changed.

To find the number of Permutations, or changes, that can be made of any given number of things all different from each other.

RULE.--Multiply all the terms of the natural series of numbers from one up to the given number, continually together, and the last product will be the answer required.

EXAMPLES.

1. How many changes can be

а b C made of the first three letters of

2 a cb the alphabet ?

3 bac Proof,

4 b ca

5 cba 1x2x3=6 Ans.

6 2. How many changes may be rung on 9 bells ?

Ans. 362880.

cab

7095

3. Seven gentlemen met at an inn, and were so well pleased with their host, and with each other; that they | agreed to tarry so long as they, together with their host,

could sit every day in a different position at dinner; how

long must they have staid at said inn to have fulfilled their i agreement ?

Ans. 110.17 ycars.
ANNUITIES OR PENSIONS,

COMPUTED AT
COMPOUND INTEREST.

CASE I.
To find the amount of an Annuity, or Pensiov., in arrears,

at Compound Interest.

RULE. 1. Make I the first term of a ger metrical ! and the amount of $1 or £1 for Que year, at the given rate

progression, per cent. the ratio.

2. Carry on the series up to as many terms as the given number of years, and five its sur.

3. Multiply the sw. thus sound, by the given annuity, and the product will be the amount sought.

EXAMPLES.

ries. *.

1. If 125 do s. yearly rent, or annuity, be forborne (or unpaid) 4 years; what will it amount to at 6 per cent. per annum, compound interest ? 1-4-1,56+1,1236 +-1,191016=-4,374616, sum of the se

-Then, 4,374616 x 125=$546,827, the amount soug ut.

OR BY TABLE II. Multiply the Tabular number under the rate, and opposite to the time, by the unuity, and the product will be the amount sought.

* The sum of the series thus found, is the amount of ll. or 1 dollar annuity, for the given time, which may be found in Table II. ready calculated.

Hence, either the amount or present worih of annuities may be rcalil found by tables for that purpose.

R

2. If a salary of 60 allars per annum to be paid yearly

, be forborne twenty years, at 6 per cent. compound interest, what is the amount?

Under 6 per cent. and opposite 20, in Table II., yar will find, Tabular number=36,78559

60 Ann, uity. Ans. $2207,13540=$2207, 13 cts. 5 m.+ 3. Suppose an annuity of 1001. be 12 years an arrears, it i: required to find what is now due, compound interest bein? allowed at 51. per cent. per annum ?

Ans. £1591 14s. 3,024d. (by Table II.) 4. What will a pension of 1201. per annum, payable yearly, amount to in 3 years, at 51. per cent. eompound ir terest?

Ans. £378 6s. II. To find the present worth of annuities at Compound Ins

terest.

RULE.

Divide the annuity, &c. by that power of the ratio sig. nified by the number of years, and subtract the quotient from the annuity: This remainder being divided by the ratio less 1, the quotient will be the present value of the an nuity sought.

EXAMPLES.

1. What ready money will purchase an annuity of 50%. to Pontinue 4 years, at 5l. per cent. compound interest?

of

the aver, of} =1,215506)50,00000(41,13513+

From

50 Subtract 41,13513 Divis, 1,05ml=05)8,86487

177,3978177 58. ld. Arts.

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and 36

BY TABLE III. }

Under 5 per cent. and even with 4 years,
We have 3,54595=present worth of 11. for 4 years.
Multiply by

50=Annuity. I

Ans. £177,29750=present worth of the annuity. 2. What is the present worth of an annuity of 60 dols. per annum, to continue 20 years, at 6 per cent. compound interest?

Ans. $688, 19 cts. + 3. What is 301. per annum, to continue 7 years, worth in. ready money, at 6 per cent. compound interest ?

Ans. £167 Os. 5d. + [II. To find the present worth of Annuities, Leases, &c. ta

ken in REVERSION at Compound Interest. 1

1. Divide the annuity by that power of the ratio denoted by the time of its continuance.

2. Subtract the quotient from the annuity: Divide the remainder by the ratio less 1, and the quotient will be the present worth to commence immediately.

3. Divide this quotient by that power of the ratio denowd by the time of Reversion, (or the time to come before the annuity commences) and

the quotient will be the present worth of the annuity in Reversion.

EXAMPLES. 1. What ready money will purchase an annuity of 507. payable yearly, for 4 years; but not to commence till two

per

cent.?
4th power of 1,05=1,215506)50,00000(41,13513

Subtract the quotient=41,13513

Divide by 1,05—15,05)8,86487

2d power of 1,05=1,1025)177,297(160,8136=£160 16s. 3d. 1 gr. present worth of the annuity in reversion.

OR BY TABLE III. Find the present value of 1l. at the given rate for the sum of the time of continuance, and time in reversion added together; froin which value subtract the present worth of 1l. for the time in reversion, and multiply the remainder by tho annuity; the product will be the answer.

jears, at 5

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