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at $2,50 per lb., for 2 per cent. commission ?-15. For 2 per cent. ?-20625. For 5 per cent. ?-3750. For 64 per cent. ?-4875. For 7 per cent. ?-5250. A. $174,37}
INSURANCE. Q. What is the allowance of so much per cent made to persons, to make good the losses sustained by fire, storms &c., called ?
Q. By what name is the instrument that binds the contracting par ties called ?
1. What will be the premium for insuring
an East India ship valued at $25000, at 15), per cent.? A. $3875.
2. What is the premium for insuring $2600, at 20 per cent. ?-520. At 30 per cent. ?-780. At 180 per cent 2481. 265 per cent. ?-689. A. $2470.
STOCK. Q. What is the general name for all moneys invested in trading companies, or the funds of government, called?
A. When $ 100 stock sells for more than $100, it is said to be above par; when for less than 100,
Q. When it is above par, what is it said to be ?
1. What is the value of $2500 of stock, at 106 per cent. ; that is, 6 per cent. advance ?" A. $2500 x 106 = $2650.
2. What is the value of $1000 ‘of insurance stock, at 95 per cent. ; that is, 5 per cent. below par ? A. $950.
3. What is the value of $1200 of bank stock, at 3 per cent. below par; that is, 97 per cent. ?-1164. At 112 per cent., or 12 per cent advance ?-1344. At 87} per cent. ?-1050. At 124 per cent. advance; that is, 112, per cent. ?-1350. A. $4908.
LUSS AND GAIN. 1. Bought a piece of broadcloth for $80; how much must I sell it for, to gain 10 per cent.; that is, 10 per cent. advance, which is 110 per cent. on the cost ? $86 X 110=$88, Ans.
2. Bought a hogshead of molasses for $50, and, 5 gallons having leaked out, I sold the remainder at 10 per cent. loss , that is, 10 per cent below par, being 90 per cent. on the cost; what did I get for it? A. $45.
3. If I pay $50 for a piece of broadcloth, how must I sell the same so as to gain 20 per cent.; that is, 20 per cent. advance, ar 120 per cent. on the cost ? A. $60.
4. Bought rum at $1,25 per gallon; and, by accident, so much leaked out, that I am content to lose 20 per cent.; how must I sell it per gallon? A. $1.
5. A merchant bought 400 barrels of flour for $3500; how must he sell it per barrel, to gain 25 per cent. ? A. $10,93%.
6. Bought sugar at 15 cents per lb.; at what rate must I sell it a ib. so as to gain 20 per cent. ?-18. So as to gain 25 per cent. ?-1875. 30 per cent. ?-195. 40 per cent. ?-21. 45 per cent. ?-2175.
50 per cent. ?-225. 65 per cent. ?-2475. 75 per cent. ?-2625.
90 per cent. ?-285. 100 per cent., or to double my money ?-30. A. $2,31.
7. Bought 100 tierces of rice, each tierce weighing 300 lbs. net, at 6 cents per lb.-1875; 30 pipes of wine for $1,124 per gallon-425250 ; 3 hhds. of rum for 90 cents per gallon-17010; 40 barrels of flour for $7} per barrel-300; and 40 bushels of salt for 7 s. 6 d. or $1,25 per bushel-50 : how much must all the said articles be sold for, to gain 50 per cent., being 150 per cent. on the first cost? A. $9971,40.
TLXVII. TIME, RATE PER CENT., AND AMOUNT
GIVEN, TO FIND THE PRINCIPAL. 1. What sum of ready money, put at interest for 1 yr. 8 mo. at 6 per cent., will amount to $220 ?
The amount of $1 for 1 year and 8 mo. is $1,10; then, $220 • $1,10= $200, Ans.
RULE. Q. How, then, would you proceed, to find the principal?
A. Divide the given amount by the amount of $1 at the given rate and time.
2. What principal, at 6 per cent., in 5 years,will amount to $650
In this example, in dividing $650 by $1,30, we annex two ciphers to 500, to make the deciinal places in the divisor and dividend equal. (See 1 LVI.)
3. What principal, at 6 per cent., in 1 year 2 mo., will amount to $642? A. $600.
4. What principal will amount to $691,50 in 2 yrs. 6 mo 15 da., at 6 per cent. ? A. $600.
5. A correspondent has in his hands $210, to be laid out in goods; after deducting his own commission of 5 per cent., kow inuch will remain to be laid out?
It is evident, that the commission which he received, added to the money laid out, must make $210; hence $210 may be considered the amoast, and the money laid out the principal; consequently, the question does not differ materially from the foregoing. In such questions as these, in which time is not regarded, the amount of $1 is the rato per cent. added to $1.
It will be recollected, that 6 per cent. is 6 cents on 100 cents, or $1; 5 per cont., 5 cents; the amount, then, of $1, at 5 per cent., is 5 cents added to $1, making $1,05; then, $210 - $1,65= $200, Ans.
6. A factor receives $1040 to be laid out in goods, after deducting his own commission of 4 per cent.; how much does his commission amount to?
The sum laid out, found as before, is $1000; then, 1040-1000=$40, commission, the Answer.
7. A factor receives $2100, from which he wishes to deduct his commission of 5 per cent.; what will his commission amount to? A. $100.
DISCOUNT. 1. William owes Rufus $1272, to be paid in 1 year, without interest; but Rufus, wanting his money immediately, says to William, I am willing to allow you 6 per cent., the lawful interest, if you will pay me now; what sum ought William to pay Rufus ?
It is evident that he ought to pay just such a sum as, pu: at interest, would, in 1 year, amount to $1272; or, in other words, such a principal as would amount to $1272. This question, therefore, is solved in the same manner as the preceding. $1272 = $1,06 =$1200, the Ans.
Q: What is an allowance made for the payment of a sum of money before it becomes due, called ?
Q. What is the sum called, which, put at interest, would, in the given time and rate, amount to the given sum or debt ?
A. The present worth.
A. The interest of its present worth for the same time.
Q. As operations in discount are substantially the same as in the preceding paragraph, what is the rule, which was there given, that is applicable to discount ?
RULE. A. Divide the given sum, or debt, by the amount of $1, at the given rate and time; the quotient will be the present worth.
Q. How is the discount found ?
A. By subtracting the present worth from the given sum or debt.
Note.-It will be recollected that, when no por cent. is mentioned, 6 per cent. is understood.
2. What is the present worth of $133,20, due 1 yr. 10 mo. hence? A. $120.
Proor. 3. What is the amount of $120 for 1 yr. 10 mo.? (Perform this example by the rule for calculating interest.)
A. $133,20 4. What is the discount of $660, due 1 yr. 8 mo. hence ?
A. $60 Proof. 5. What is the interest of $600 for 1 yr. 8 mo.?
A. $60. 6. What is the discount of $460, due 2 yrs. 6 mo. hence ?
A. $60. 7. What is the present worth of $1350, due 5 yrs. 10 mo. hence ? A. $1000.
8. Bought "goods to the amount of $520, on 8 mo. credit; how much ready money ought I to pay as an equivalent? A. $500.
9. Bought goods in Boston, amounting to $1854, for which I gave my note for 8 mo.; but, being desirous of taking it up at the expiration of two months, what sum does justice require me to pay ? A. $1800. 10. What is the discount of $615, due 5 mo. hence ?
A. $15. 11. What is the present worth of $1260, due 10 mo. hence ?
A. $1200. 12. What is the present worth of $1272, due 2 yrs. hence, discounting at 3 per cent.? A. $1200.
13. What is the present worth of $51,50, due 6 mo. hence ?50. Of $204, due 4 mo. hence ?-200. Of $13000, due 5 yrs hence ?-10000. Of $9440, due 3 yrs. hence ?-8000.
A. $18250. 14. What is the present worth of $515, due 6 mo. hence ? 500. Due 1 yr. hence ?-485849. Due 15 mo. hence ?-479069 Due 20 mo. hence ?-458181. Due 4 yrs. hence ?-415322.
A. $2348,421 +.
1 LXVIII, TIME, RATE PER CENT., AND INTEREST
BEING GIVEN, TO FIND THE PRINCIPAL. 1. What sum of money, put at interest 1 yr. 8 mo. at the rate of 6 per cent., will gain $20,60 interest? The interost of $1 for 1 yr. 8 mo. = 10 cts. ; then $20,60+$,10 = $206, Ans
RULE. Q. How, then, would you proceed?
A. Divide the given gain or interest by the interest of $1 at the given rate and time; the quotient will be the principal required.
2. A certain rich man has paid to him every year, $48000 interest money; how much money must he have at interest? Of what principal will gain $48,000 in 1 year, at 6 per cent. ?
A. $800000. 3. If a man's salary be $12000 a year, what principal at interest for 1 yr. at 6 per cent. would gain the same?
A. $200000. 4. Paid $45, the lawful interest on a note, for 2 yrs. 6 mio.; what was the face or principal of the note ? A. $300.
1 LXIX. THE PRINCIPAL, INTEREST, AND TIME,
BEING GIVEN, TO FIND THE RATE PER CENT. 1. If I have $2000 at interest, and at the end of the year ! should receive $120 interest, what rate per cent. would that be?
The interest of $2000 at 1 per cent. for 1 year, is $20; therefore, $120+ 20 =$6, that is, 6 per cent., the rate required.
RULE. .Q. How, then, do you proceed to find the rate per cent. ?
A. Divide the given interest by the interest of the given sum, at 1 per cent. for the given time; the quotient will be the required rate.
2. If I receive $60 for the use of $600, 1 yr. and 8 mo., what is the rate per cent. ? A. 6 per cent.
3. If I pay $200 for the use of $2000 for 2 yrs. 6 mo., what is the rate per cent. ? A. 4 per ceni.