tracting the amount from the amount of the whole note, just balances the excess of interest found on the note, and also lessens the note by a sum equal to the payment. 76. A note of $546,60, was dated December 25, 1823, on which were the following endorsements: January 3, 1825, $110, and August 4, 1825, $20,50; what was due July 31, 1826, allowing interest at 6 per cent.? Ans. $489,737. 77. A merchant bought goods to the amount of a thousand dollars, and gave his note, dated Jan. 1, 1824, on interest after 90 days. Six months after the date of the note, he paid $560; and five months after the first payment, he paid 406 dollars. What was due August 23, 1826, computing interest at 6 per cent.? Ans. $63,525+. 78. A bought a horse for seventy-five dollars, and paid two-fifths at the time. The remainder he paid in fifteen dollar payments, and the interest, on the whole, at four and three-fourths per cent., at the last payment. The time intervening between the payments was 30 days. What was the last payment? Ans. $15,351+. 79. A note of $1200,67, at 7 per cent. interest, was dated November 7, 1823, on which the following partial payments were made: April 6, 1824, $371,22, January 3, 1825, $197.00, What was due July 4, 1826, and what part was interest? Ans. { The sum due, $286,405+, of which $123,305+was interest. Remark.--The methods of computing interest on notes when partial payments are made, vary in different sections of the country. The student, however, will find little difficulty in computing interest by any method, after he has acquired a thorough knowledge of the general principles. COMPOUND INTEREST. Interest is compounded when the interest on the principal for one year, or the time agreed upon, is added to the principal, and the interest east on the sum for another period of time. Compound interest is not sanctioned by law, but is frequently computed by the consent of the parties concerned. There is no difference between the methods of casting compound interest and simple, except adding the interest at the end of a specified time, and making the sum a new principal for another period of time. If no particular agreement is made, the interest is generally added to the principal at the end of each year. 80. What is the amount of a hundred and ten dollars, for four years, at six per cent., compound in terest. Operation. 6,60 interest for the 1st year. 110, 1 16,6 0 principal for the 2d year. 0 6 6,9 9 6 0 interest for the 2d year. 1 1 6,6 0 1 2 3,5 9 6 principal for the 3d year. 7 1576 interest for the 3d year. 1 2 3,5 9 6 131,0 1 1 principal for the 4th year. 06 7,8 6 0 6 6 interest for the 4th year. 1 3 1,0 1 1 1 3 8,8 7 1 amount for 4 years. The decimals of a mill are omitted. 81. What is the compound interest of $409,53, for 3 years, at 5 per cent. ? The interest will equal the difference between the whole amount and the given sum. Ans. $64,552+. 82. What is the amount of $117,06 for 2 Y. 5 md; 19 days, at 6 per cent. compound interest? Ans. $135,22. 83. What was the amount of a note of $1005, Oct. 1, 1826, bearing date Dec. 12, 1823, at 5 per cent. compound interest? Ans. $1167,973+. PROMISCUOUS QUESTIONS IN PER CENT. 1. Estimating the year at 360 days, what is the per cent. for each of the following periods of time, when the per cent. for a year is 6; 7 days, 17 days, 23 days, 1 month and 5 days, 2 months and 19 days, 7 months and 16 days? (See Note 6, Sect. 8.) Answers,-,00116+,,00283+,—,00466+, -,00583+,01316+,-,03766+. 2. At 6 per cent. for one year, what is the per cent. for 34 days, estimating the year at 365 days? 34 365 34 days equal fore, for 34 days is of a year. The per cent., there3 of 6 per cent., which is 8 of 1 per cent., or changed to a decimal-,00558+. 65 3. If the per cent. for 365 days be 5, what would be the per cent. from Jan. 1, to June 17, of the same year? Ans. ,02287+. 4. A man bought a quantity of cotton for 800 dollars, and sold it so as to gain 9 per cent. For how much was the cotton sold? Explanation. He gained 9 cents on each dollar of the purchase money, consequently, multiplying 800 by 9 cents, the product will be the gain. Ans. $872. 5. A buys a quantity of rice for $179,56; for what must he sell it to gain 11 per cent. ? Ans. $199,311+. 6. A merchant buys 117 hats for $325; at what must he sell the hats a piece to gain 12 per cent.? 325 times 12 cents added to 325 dollars, will be the amount for which he sells the whole. Ans. $3,111+. 7. IfI pay 16 cents a pound for 137 lb. of butter, what must I sell the whole for, to gain 15 per cent.? Ans. $25,208. 3. H bought a quantity of cambrick for 131 dollars, and sold it for $157; what did he gain per cent.? Explanation. The difference between what he gave and what he received, is the whole gain, and the whole gain divided by the number of dollars he gave, will show what was gained on each dollar, which will be the per cent. 157-131 26 the whole gain; and the per cent, is the quotient of 26 divided by 121. 26 The per cent. may be expressed by a fraction thus, of a dollar, which reduced to a decimal equals $0,198+the answer. 9. A merchant bought a quantity of salt on board of a vessel for 41 cents per bushel, and paid 2 cents per bushel for truckage. He sold the salt for 57 cents per bushel; what did he gain per cent. ? Ans. ,3372+. 10. A man bought an ex for 39 dollars, and sold it for 381; what did he lose per cent.? When the price given is dollars, and the difference between the giving and selling price is cents, the price given must be reduced to cents by adding two ciphers. The loss per cent. in the last question isot, or, ,0128+the answer. Note 10.-The difference between the cost of any quantity and the price for which the same quantity is sold, divided by the cost, will give the per cent. gained or lost, whether the price for which the quantity is bought and sold, be dollars or cents. If 2 dollars be divided by 10 dollars, the quotient is 2 dimes, or 20 cents, that is, 20 cents, or 20 per cent. on each dollar in the divisor. The quotient of 2 cents divided by 10 cents, is 2 mills,that is, 2 mills for each cent in the divisor; but if we multiply the divisor, 10 cents, by 100, and 2 cents the dividend by 100, the quotient will be the same as in the other example; 2 mills, therefore, gained or lost on 1 cent is the same per cent., as 20 cents gained or lost on 1 dollar. 11. P buys 8000 pounds of tobacco for $850, and pays cash for. For the remainder he gives a note payable in 6 months, on interest at 6 per cent. after 30 days. For what must he sell the tobacco per pound to gain 25 per cent. ? Ans. 13 cents and 4+mills. 12. A merchant bought 3 T. 4 cwt. of iron, June 21, 1825, for 5 dollars 25 cents per hundred, and sold it Dec. 6, following, for 6 dollars per cwt. He 63 paid 7 per cent. for the use of the purchase money; what did he gain? Ans. $63,872+. 13. If I buy cloth at 26 cents per yard, what must I sell it for to gain 10 per cent., if I pay 6 per cent. for the use of the purchase money? bar Ans. $0,301+. 14. D bought a quantity of flour for $4.50 per rel, but it proving bad, he is willing to lose i5 per cent.; for what will he sell it per barrel? Ans. $3,825. 15. A man sold a piece of cloth for 25 cents a yard, and by so doing he lost 20 per cent.; what did it cost him per yard? 80 Explanation. He sold it for % of what it cost him; or, in other words, the price for which he sold is in the same degree less than the cost, that the numerator 80 is less than the denominator 100. 8 0 Were we to take of the cost, the result would be the price for which he sold, but if we invert the terms of the fraction, thus, 10%, and multiply 25, the price for which it was sold, by 10, the result will be a 809 |