Nicolas Pike.

# A new and complete system of arithmetick. Composed for the use of the citizens of the United States online

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the third payment, or JC160 for 10 â€” 8 or 2 months, whieh is â€” â€” -*

^^ 100x6X8-^ , I?0x6x5^ 160X6X10 - H Â«r ^ .1.

Then, ~ 4. j^ ^ ^^00 ; â€˘ ^^^^^'^^9-r

cent, and 100 will be factors common to every term m every case, they may bo
expunged from every term, and then we have,

100X8â€” â‚¬+ 120x5â€” 7=160x 10â€”8. From this equivalent exprasskm, it is
easy tq find the equated time; for, 100x8â€” 100x6-fl20xeâ€”180x7=iea
XlO â€” teOxn, or 100x8-fiaQx8-fl6ax8=10Ox6~hlgQx7-f-iWxlOÂ» or,
8 XKKH- 11*04-160=100x6+ 130x7+ 160X10, and -
8=100X6+120X7+160X10 ^. ,..,,., ^ ^ ,

â– â€˘> " ^ ' . . ^, . ,^: r which IS the rule. The same may be shown

ilRr+lxiU-*-loU

in every similar case, and the general rule inferred.

This rule is manifestly incorrect. The true rule will be given in Kqualion oT
Faymcuts by Dcrrmal*'.

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EI^UATION 0f PAÂĄfifEWT9 BX PECIMALS. Â«9I

beiweea them tbat P shÂ«H iaakÂ« present pay of hia whole (jÂ«kt,
add that Q, shall pay his so mach (be sooDcr, as to balance that fa-
iro0r ; I denand the tiipe at w^cb (jLnuat p4y tt^e pt50 recliQainic
i^'m^ie interests

60X4Â»200

iopxa=8GO^

60+100=15|0)100|Q(6| months^ P*s equaled tiAe.
90

10

D. mo. D. mo* mo. mo. mo.

As 150 : 6| :: 260 : 4. Then, 10â€”43=6 Cime pf^'s payment.

2. A merchant has 1201. dne to him, to be paid at 7 months ; but
the debtor agrees to pay ^ ready money, and ^ at 4 months ; I de-
mand the time he must have to pay in the rest, at simple interest,
\$0 that neither party may hafe the advantage of the other ?

; Debt ÂŁ120

â€˘|,:^60 mast be. paid down.
^sx40 mast be paid at 4 months.
^=20 unpaid.
Now, as be pays 601. 7 months, and 401. 3 months bejbre they are
respectively due, say, as the intenest of 201* f ' Â» kr to 1

month, so is the ^um of the interest of 601. s, and of

401. for 3 months, to a fouflh number, which, ac months,

will give the time for which (he 201, ought to

Ans. 2 y months.

3. A merchant has \$120IG| due to tiiP* to be moi^ths,

^ at 3 months, and the rest at 6 cnonths ; but ^ ^ jgr^es to

pay I down : How long may the debtor detain the other half, so
that neither party may sustain loss 2 '

Now ^9 i was paid 4^ months before it was due, it is reasonable
(hat he should detain the other |, 4^ months after it became due,
which added, gives 8| oiooths, the true time for Ihe second pay-
ment. Equated tiala'Â»4| aioatl(9.

. EqUATiOJi' OF PAYJifENTS BY DECIMALS.

Rule.*
1. To the sum of both payments add the continual product of
(he first payment, the ratio, and (be time between the payment^,
and call thi^ the first numbe^'.

* Suppose a sum of money be due immediately, &nd another at ^e expiration
of a oerUiufSFea time forV&nl) and it is proposed to find a time, so that' neither
party jhiill sustain loss.

Now, it is plain that the equated time must fall between the two payments ;
and that what is gotten by keeping the first debt after it is due, should be equal
to what it lost by ^jing the second debt before it is due ; but the gain arising

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tn EQpATION' OF PAYMENTS BY DECIMALS.

9, Multiply twice the first payment by the ratio, aad call this the
secood Dumber.

3. Diride the first number by the second, and call the quotient
the third ntimber.

4. Call the square of the third number the fourth number.

5. Divide the product of the second payment and time between
the payments by the product of the first payment and the ratio, and
call the quotient the fifth ntunber.

6. From the fourth number take the fifth, and call the square
root of the diftreoce the sixth number.

7. Then the difference of the third and sixth nombers is the
equated time, after the fint payment

Examples.
There are ^100 payable io 2 years, and {106 at 6 years hence ;
what is the equated time, allowing simple interest, at 6 per cent.
per annum 7

Ist payment=]00 1st payment 100

Ratio^'06 Multipiy by 2

600 200

Time between the paymentsâ€” 4y8. Mult, by the ratio= 06

24 12'00^2dQua.

Div. by the 2d num.=12)230=l8t number.

19166+=3d number.

19-166+

3d number 8quared==367-335556=4ih number.
2j)payroenl=l06
Multiplied by the time=^ 4

Ui payment molt, b, tbe ratio=6)424^ | ''S^.ti;;â„˘*?:^;"^^

70^66+c=5lh number.
From the 4th number=367 3S5666
Take the 5lh number= 70 666666

296 668890( 1 7-224sqr.root=6th nuai.
Carried up.

from the keeping of a smn of money after it is due, is evidently eqtiÂ«l to tbc in^
terett of the debt for that time : And the low, which ia sustained by the paying
of a sum of money before it is due^ is evidently equal to the dis^otmi of the debt
for that time : Therefore it is obviouA that the debtor must retain the sum im-
mediately due, or the first payment, till its interest shall be equal to the diteount
of the second sum for the time it is paid before due ; because in that case the g;aiu
and loss will be equal, ftnd consequently neither party can be a luscr.

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EXCHANflE. 293

From the 3d nuinber==:191 66 Brought up.
Take the 6(h Mamber= 17-224

100+10e+100X-06x4 100-1-106+ 100X1)6X4
Or,

I-942=s=equated time from the firn pay-
ment ; therefore 3 942 years
=3y. Um. 9d.^fvhole eqnat-
ed time.

i

106X4

â€” 1 =1-942.

100X2X-06 ioox2x*06 j loox-^ej

2. There are ^100 payable one year benoe, and }1()6 to be paid
sis years hence ; what is the equaled time, computing interest at
6 per cent. ? Aos.

3. A debt of \$1000 is to be paid, one half in three years and
the other half in 6 years ;'what is the equated time for paying
both, computing interest at 7 per cent ? Ans.

EXCHANGE.

THE object of Exchange is to ascertain what sum of money
ought to be paid in one country for a sum of different denomina-
tions or of different relative value received in another, according
to the course of exchange.

The par of exchange respects the intrinsic value of the money
of different countries compared with each other. Thus a pound
sterling is equal to 4 dolls, and 44 cents in the United States ; the
mark banco of Hamburgh, to 33^ cents ; 40 marks banco to ÂŁ3
sterling. If the exchange be made at the intrinsic value of the
money of different countries, it is said to be at par; but if the mo-
ney of one country be estiniated. at less or more than its intrinsic
value, the exchange is said to be above par^' or below par,*

Owing to ehanges in the course of trade, to demand for money,
to variations in the relative value of gold and silver, &c. the rela-
tive value of the money of two countries is liable to frequent chao-
ges. Hence the course of exchange^ or the current price of ex-
change, must vary with these circumstances, and be sometimes
above, and sometimes below, par. Tables of the course of ex-
change are published daily in the great commercial cities.

* The RqW utukr Redaction of Coins are founded on tfaie par of exchange,
For thÂ« redaction of the Money, and Measures of most commercial coiualries to
Federal and Sterling; Money, aiid American Measures, see also the Tables of
Money, Length, Capacity and Weight.

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iÂ»f EXCHANQE.

I. OF GREAT BRITAiN.*^
The deDominatioDt afse pouods, sMHiogs^tod peace.

EzAMPtES.

1. What h the amoQDt id Federal MoDej of a Bill ef E^^chaoge
6n a merchant at Liverpool of ÂŁ135 sterfing, aold in New York ^
I per cent, adrance ? ÂŁ \$ c.

133=359111^

2-9Sff sspj per cefit-

Amount J59406f Ans.

^. In Aug. 1821, Bins on London, bore atBostpo a prenftium of 8^
percent ; what is the aioount of a btH of exchan^ of X250, at thii
rate, in Federal Money^ and what is the value of a pound sterling
at tbhÂ» course of exchange ? Aos. Amount \$1205 55fct\$.

Value of a pound sterling \$4 82|cts.

S. A BiH of Exchange on London of ÂŁ90 sterling, was sold at
New York, at 36 shiHings New Yofk currency per pound ^erling ;
what was its amount ^ the currency of New Yprk> and how much
Above or bâ‚¬law par ?

â€˘As 1 : 36 :: ^ : 16? N. Y. currency.
N^w ÂŁ9 sterHng:=: jBie N. Y. currency, or SOs. sterling=35f N. Y.
currency. But 36â€” 35f a=jÂ«. N. Y. currency, the gain o|i every
pound sterling, or ÂŁ2 N. Y. in the whole.

TheD, as 36^. : J :: 100 : 1^ per cent, abore par.

Or, f62 - Â» : 2 :: 100 : l| do. '

4. The invoke of goct^, sunonnting to ÂŁ170 lOs. sterling, h
aold at New YoHt at 25 per cefK. advance ;t what is the amount
m Federal Money ? 4ns.

* .The I^tilcs OD whiob the opemtknAs of Exchu^ tktt peiform^ Bra obti-
fitts from the rules for Rcduotion of Coim, and the Rale of Three.

t To reduce sierUiig' ateuey to the currciicy Â«f New Efig^land, whea theis i^
Â«. (;eÂ«tun per cent, advance, merchaiits use the foUowiog method. '
For 124 per cent advance, l&ultiplf the sterling by 14

\$0 1|

S5 - - ai

3ii :...-â€˘.. . i|

50 ^2

Â»n - - n

?oo . ga

125 3^

150 ^ . . 31

175 - ..-.- 25.

200 - /

These multipliers are thus ibnncd. Let the advance be 25 per cent oo ÂŁ100;
100 500

4 4

is to be reduced to New England currency by increasinfir it by one thiKl ^ itael/.

500 500 2000 o ^

TlwM â€” x^-=-~-=sl6â‚¬J pounds ; which is evidenUy the same as to mul-
tiply 190 by 1 J. In the same way may the otiier multipliers be fbucd.

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EXCHANGE. t95

5. A Ml of BtclMDgÂ« of ÂŁ15 IGb. ia ^M Ai Boetoo at 26Â«. New
England cnrrertcy per ponnd sterling ; what w the yalae in Fed-
eral Money of a pound sterling at this r^teof exchange? Ans.

2. OF FRANCE.

The money of aoconnt is li?res, sols, and detiiers.
12 deoiers tbske 1 sol or shilling.
20 sols 1 livre or pound.

The livre is estimated at 18^ <:eiits in the U. S.
The crown of eichange is 3 liTrei, or livreS tbnniois, ahd ts
equal to 55| cents.

The present money of aecoont k francs and centimes et hiui*
<lTedthS. 80 franc8=^8i livres, or k franc^}^ livre.

1 . To reduce francs to lirres, or the contrary, multiply the francs
by 81 and divide the prodoct by 80 for livres ; or OMiItiply the 11-
vres by 60 and divide the product by 81 for francs.

2156x81
Thus 2156 francs=: ^ â€” ^=2183 UHe^ 19 sols. And 2341

2341x80
It vres =^ ' o| =2312 francs, 09Jf cetitimes.

2. To reduce livres to dollars and centa ; mnlltply the litres bf
the centa in a Irvre at the course of exchange. *

EkAMTLKB.

i. If the livre be 20 cents in exchange, what is the Miooot of
9160 livres io Federal money, and what is the per cent above pat
it this etohange ?

Ans. Amount is {430. And above par 8^ per cent.

2. If the livre be 1^ cents in exchange, required the amount of
S580 livres 16 sols, in dolb. and cents, and the rate per cent, be^
low par.

Ans. 644'54^*y cents, and 2|4 per cent, below par.

3. If a crown be valued in exchange at 18d. sterling, required
the livres in JSIQO sterling, and tbe amount also in Federal money
at par. d. liv. ÂŁ Itv.

As 3 livreiis=l crown, 18 ; 3 :: 100 : 4000 afid 4000X1 8|Â«!:jj740.

4. In 2583 francs, how many dollar;^ ?

2583x55iÂ«=I433doKs. 56^ cents.

5. A bill of exchange on a merchant in New York of {730 65cts.
wa5 bought at Paris at 1} per cent, advance ; what is the amount
in franc<*, and what was the estimated Talue of a franc at this ex-
change ? Ans.

3. OF SPAm.
8^ qiiartosÂ«a^34 marar. 1 rial plate.
8 rials platÂ« 1 piastre or current dollar.

375 maravadies 1 ducat of' exchange.

Hard or plate dollars ^re 88^ per cent, above ri^rr^ar dollars or
money of vellon, or

Digitized by

^96 EXCHAN6E.

100 rials plate t=ia8^^ riaU vellon.
17 do. =^32 do.

The rial plale is 10 cents, and the rial vellon 5 cents in tlte U.
States.

To reduce rial* plate to rials vellon, or the contrarj, multiply
the rials.plate by 32 and divide the prodoct by 17, for rials vellon ;
or Multiply the rials vellon by 17 and divide the prodnci by 32, for
rials plate.

1100x32
a. Thos 1100 rials plate=' â€” yj rials vellon s=>2070fj Ans.

100X17
And 100 rials vellon= â€” -^"^ rials plate=3:53| rials plate. Ans.

. Note. The rules to reduce rials plate or vellon to Federal Mo-
ney are obviojus and need no examples.

2. In the sale of a bill of exchange of 1563 rials plate, the rial
plate was estimated at df cents ; how much per cent, was the rial
below par and how much the loss ?

Ans 4| per cent. \$6*94| the loss.

3. If the piastre be valued in exchange at 81 cents, what is the
per cent, above par on a bill of 1672 piastres 5 rials plate, and what
i& ti&e advance on the bill in Federal Money ? Aos.

4/ OF HAMBURGH.

12 denierd=2 grotes make 1 shilliog lubs, or stiver.
16 shilling !ubs=32 grotes 1 mark banco.*
' . ' ^3^marks 1 rix dollar.

Or, 12 grotes or pence Flemish make 1 shilling Flemish.
20 shillings Fl.=7^ marks 1 pound Flemish.

A mark is ^ of a dollar, or 33| cents in the U. States, and ih&
Rix dollar is equal to the Spanish dollar, or 100 cents.
The mark is 2| shillings Flemish*

The Bank money of Hamburgh is superior to the currency at a
variable rate per cent.

1. To reduce marks banco to dollars, divide the marks by 3.

3437
^fhus 3437 mark8=-3-dolls.=J1146 CCJcts.

2. To reduce pounds Flemish to dollars, muliiply the pounds by

5, and divide the product by 2 for dollars. Thus, to reduce 175

175*5x5
pounds Fl. and 10 shillings to dollars, n â€” dolls.â€” \$438-75cts.

3. To reduce Hamburgh money to sterling, use the following
proportion ; As, the value of a pound sterling at Hamburgh is to
1 pound, so is the Haa>borgh sunx to the sterling required.

1. When the pound sterling is 33 shillings Flemish, what is the
value of ÂŁ1567 10s. Fl. in sterling money ?
9. ÂŁ J&Fl. ÂŁ sterling.
As 33 : 1 :: 1567-5 : 950

* Banco is money placed in banks of deposit, and is not to be drown out,btit
is transferred from one pCRon to another for the payment of contracts.

Digitized by

POLICIES OF INSURANCE. 5Â»7

^. Redact 2560 marks B shivers to sterlin^f, at the rate ofSS^ shil"
iiDg9 Fl. per pound sterling. Ati\$. X204*16'9 6d. sterlings

3. When the poand sterling is 34 shillings Flemish, what is tbe
per cent^ below par ? Ans^ 4| per cent.

4. To reduce current to Bank money, use the following propor*
tion. As 100 marks with the rate added is to 100 bank money, so
is current sum to the bank money required.

1. Reduce 360 marks current to bank moneys when rate or agio
is 20 per cent.

As 100+20 : 100 :: 360 : 300 bank money, Ans.

2. When the rate or agio is 18^ per cent, what is the value of
3769 irtarks 8 stivers current in bank money ? Ans.

3. If 375 marks current are estimated at 320 marks bank, what
is the rate per cent ? Ans.

OF CALCUTTA.
12 pice make 1 anna,
16 annas 1 rupee.

The Bengal rupee is estimated at 50 cents in the United States ;
in exchange it is usually 3 or 4 cents less.

100 sicca rupees are equal to 116 current rupees. *

1. Reduce 187 rupees 8 annas to federal money at 46^ cents
per rupee. Ans. \$S9 06J cents.

2. Reduce ^367^ to rupees, (he rupee being valued at48cents^

Ans. 763 rupees, 15 annas, and 4 pice.
Note. From the exchange value of the money of difierent coun-
tries, and from the Table of Money of commercial courrtries, im-
mediately before the ** Chronological Prpblems," the student will
be able to derive particular rules for making all the exchanges of
money, which may be necessary in business.
%

POLICIES OF INSURANCE.

INSURANCE is an assurance or security by a contract, to in-
demnify, for a specified sum, the insured for such losses as the
property may be exposied to, for a certain time.

The insurer pr nnderTatriter^ is the party that is bound to indem-
nify for the loss sustained.

The premium is the compensation paid by the insured for the
insurance.

The policy is the document by which the contract of insurance is

Goods are s^tid to be corvered, when their value and the premium
and other charges are insured.

If the loss do not exceecl^v^ per cent, th.e underwriter is free,
and the loss is borne by the insured. Particular average, is the
proportioning of such losses as ^tUc from ordinary accidents at sea,

O o

Digitized by

S9^ POLICIES 01*^ INSURANCE.

â‚¬inoDg the proprietors of the prop^rtj which goffers (he ilijtft^*
General averixgef is the proportion to be paid by all the owners of
ship aii4 cargo, for losses necessary to preserve the rest, soch as
cottiog away masts, kc. throwing part of the cargo overboard, and
the like. As this is done for the oomdion good, it is to be borne
by the owners of the ship and cargo, in proportion to the vakie of
the property possessed by them severally.

In computing general average for masts, he* to replace those
cot away, one third is usually deducted from the expense, be-
cause the new articles may be supposed better than the old

Unless the property is altered the insured is not indemnified^ in
case of total loss, but in (he proportion contained in the policy ;
and, in cage of a partial loss, the insured is to be indemnified only
in the same proportion.

Note. General average is computed by the Role for Single tt\-
lowship. See examples 19 atid 20 undet that rule*

CASE 1.

WheA Ike premium^ ai a certait rate per c^nty for insuring a Hitriy is
required^ the operation is tM same as ih inieresiy or commission.

Examples.
1. Wliat is the premium upon 6371. 158. 9d. at 6^ per cent. :

537 16 9
Si

3226 14 6
i= 268 17 lai

34196 13 4}
'20

19|12
12

1|48

1|94 Ans.ÂŁ34 19s, l}d. fteariy,

2. What is the premium upon ^375, at 7| per cent. ?

Ans. J28*l2a.

CASE II.

Tojind the sum for ixhich a policy should he taken out to cover a

given sum.
Rule. Take the premium from 1001. or ^lOO, and say, As the
rentainder is to 100, so is the sum adventured to the poFrCy.* Or,

â€˘ It is plain, that the polity should be equal to the insurance and the sum in-
â€˘ured. Henee at 8 per cent a policy of j&lOO would secure only ÂŁ92. In order to
yeeovcr j^OS, therefore, the policy must be taken out for jSlUD. liMwe the rv^ vi

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|>Of.ICIÂŁS OF INSURANCE. 299

lo decimals^ take thi^ preaiiom frpm 100, annex two evpbera (o
tint sum to be corered, ^o^ 4*^^^^ ^y ^^ reqnaiuder for the policy.

1. It 18 required to cover 7\$9l. pten^iurp'S percept. : For what
^um must the policy be taken V '

100
8

92 : 100 :: 759
100

ÂŁ

92)76900(826 Anf.
736

230
184
r 76900

460 Of, =ÂŁ826, Ana. ^before.

460 92

2. A merchant ^^nt ^ vessel and cargo to sea, valued at 5^760 :
What som mnet tb^ policy b^ takei^ out for, to cover this property,
premium 19| per cent. ? Ans. ^7156 28c.

CASE in.

Whef^ a policy t> taken out for a certain si^m in order to covp- a
given sum.

To fim| the premium, say, as the policy is to the covered sqm ;
80 18 loot, (or {100) to a fpiiftfi number, which, being taken from
lOQ, will leave the premifini. pr,

In decimals^ divide the sum covered, with tifO cypher! anf^ied,
by the policy ; subtract the quotient from 100, the remainder is the

1. If a policy be taken out for 12501. to cpver 60QI. What it the

oWioQi. 19ie diSennce bÂ«tif ecn 100 and the ra(Â« per i^ent will be the first
term, 100 the second, and the sum to be ioflured the third term of a proportion,
and the rule is merely a particnlar application of the Ri^e of Three. In the first
eiEample, tjie proportion would stand thus, 100-~8 ; lOO :: 759 : the poli<J3r=

lUuLg -=^^- ^^'^ ^^'^ premiuxvon je825,i,, -^=ÂŁ66, and 66+

7593=j^35, the policy. The role for deeimaU is evidently a contrpcUon of this
rule.

In Case III. the last three terms ip the preceding: proportion are given to find
the rate. Those three terms evidently g^ire the differenice betVeen 100 and the
rate, and the rule is obvious.

In Case IV. the first two terms and the last term of the prepeding^ proportion
are s^iven, to find the third term or joun covered, and the reason of the operation
Js pliin ffom the conÂ«iderulion of that proporlJon.

Digitized by

:kh> policies of insurance.

1250 : 600 :: 100
100

1250)60000(40 and JClOOâ€” 40=:jE60, Aos.
50000
Or, â€”â€”=40, &c. as before.
1250
2. If a policy be taken out for J781-25, to cover ^626 : Requir-
ed the premium per cent. ?

i c. \$ \$ \$ c.

As 781-25 : 625 :: 100 : 87-50. And, 100â€” 87-6= 12-5, or I2i

Or, â€” =87Â»5, &c. as before.
781-25

CASE IV.

fVhen the policy for covering any sum and the premium per cent, are
givenf tojind the sum to be covered*
Rule.
Deduct the premium ^er cent, from 100, and say. As IQO is to
the remainder, so is thÂ« policy to the sum required to be covered.
Or, In decimals^ Multiply the policy by the reipainder found a.8
before, and point olfftwo right band places in the product for the an-
awer-

EXAMPL^S.

I. If a policy be taken out for 12601. at 60 per cent : What* is
the adventure or sum to be covered ?
100
60

100 : 40 :: 1260 Or, 1260x100â€”60=50000, and,

40 pointing off two places, 50000

ÂŁ Ans. as before.

100)60000(600 Ans.
2. If a policy be taken out for ^781 26c, at 12J percent, requir-
ed the turn covered ?

78 1 â€˘26X100â€” J 2^

As 100 : 100â€” 12J :; 701-26 : =^626, Ans.

100

Or, 781-25X100â€” 12 6=62500 ; and 626-00, Ans. as before.

CASE V.

When a given sum is adventured several voyages round from one place
to another y either at the same, or different risks, from place to place,
and it is required to take out a policy for suck a sum as will cover
the adventure all round, \$upposing the risk out and home to be equal
and tantamount to the several given risks.

Rule.
1. Raise 1001. or glOO to that power denoted by the number of

risks, and mottiply the said power by the sum adventured, (or to

be covered) for a dividend*

Digitized by

POLICIES OF INSURANCE. 301

.\$. Subtract the several premiums, each, from 1001. and multi-
ply the several remainders cobtinually together for a divisor, aod
the quotient, arising from this division, wUI give the policy to cov-
er the adventure the voyage round.*

Example.

per cent, from thence to Guadaleupe, at 4, from thence to Nantz, at
5, and from thence home at 6 per cent. ; For what sum must he
take out a policy to cover his adventure the vogage round, suppos*
ing the rjsk to be equal out and home^ and tantamount to the Sev-
eral given risks ?

100 X 100 X 100 X 100X1500

â– = == â€” =gl803-835, Ans.

100â€” 3X100â€” 4X100â€” 3X100â€” () ^

CASE Vl.

When a given sum is adventured several voyages rounds as %n the last
casCy either at the samey or different risks^ from port to porty and
pie premium for the^ voyage round is required^ tantamount to the
several given rates per cent,

* It is evident that the polity to be taken out for the first voyage becomes the
sum for which a policy is to be taken out for the second voyage, and so on.
Hence the examples of this case are to be solved by the rule for Case II. making
the sum in the policy for the first voyage, the sum for which a policy is to be tak-
en out for the second voyage. Therefore the operation on the g;iiren example
would be as foUow4.

.r^ o ,n^ .rnn 1- t ^-x 100X1500 â€ž 100X1500

100â€”3 : 100 t: 1500 : pohcy for 1st voyage=:â€” -â€” - â€”-. Now as â–  â–

100 â€” 3 100â€” -J

is the sum to be insured on the second voyage, we have,

.^ .. ,/^ 100X1500 ^^ ,. 100X100X1500

100â€”4 : 100 :: â–  , â€ž - ; 2nd pohcys:^

^"^^^â€˘^ 100â€”3 X 100â€”4
. ..^ . .r^ 100X100X1500 ^^ ,. 100X100X100X1500
And 100â€”5 : 100 :: ' : 3d policv= r ^ â–  -> .

100â€”3X100-^ 100â€” 3X100 â€” AX 100â€” 6

* ,,^ . .^ 100X100X100X1500 ^. ,.
And 100â€”6 : 100 :: . - . . . " - = 4th pobcy=

100â€”3X100â€”4X100â€”5
100X100X100X100X1500 100*X1500

100â€”3X100 â€” 4 X 100â€”5 X 100â€”6 100â€” 3x 100â€”4 X 100â€” 5X 100â€”6
which is the Rule. The sam6 may be shown by the Double Rule of Three, thiis,

100â€”3 : 100 :: 1500 ! "1 â€˘ ,. 100* X 1500

100â€”4 : 100 :: : I "*Â® poÂ»cy=^

:)â–

lOQâ€”S-lOO- â€˘ f 100â€”3X100-^X100â€”5X100â€”6

100-6 i 100 *:â€˘. : J =\$1803 83c. 5m.

It is plain that however numerous the voyages, the power of 100 must be equal

. to their number, and tliat the divisor must always be the continued product of

the differences between 100 and the several rates of insurance. If the rate of in-

, ,, , lOO^Xl.'^C'O

surance had been the same on each of the voyaÂ«;os, then the policyr-z â€” â€” -

ir the rate had been G per cent.

Digitized by