RULE. 177. Multiply the sum on commission, or insurance, by the rate per cent., and the product will be the commission, or premium (162). QUESTIONS FOR PRACTICE. 1. At 3 per cent. commis- 3. At per cent. what will sion, how much must I allow th insurance of 738 dolfor selling 525 dollars worth lars ? of goods : $738 X.005—$3.69. Ans. $525 X.03—$15.75. Ans. 2. What is the commission 4. At 31 per cent. what on 827 dolls. and 64 cents, at must I allow my broker for 25 per cent. ? purchasing $2525 worth of Ans. $20.691. goods ? Ans. $88.371. INTEREST ON NOTES AND BONDS. 178. The methods of computing interest on notes and bonds differ in different places. Those in most general use are the following: 1. Find the amount of the principal up to the time of payment, and also, the amount of the endorsements from the time they were made up to the time of payment; deduct the latter from the former, and the remainder will be the sum due. This method is evidently erroneous; for suppose a note be given for 100 dollars with interest, and 6 dollars be paid at the end of each year for four years, which is endorsed on the note. Now the interest of the principal for this time is 24 dollars, just equal to the sum of the payments; but by this method the several payments all draw interest from the times they are made, the first 3 years, the second 2, and the third 1.=1.08+72+36= $2.16, which goes towards paying the principal, and in this way any debt. would in time be extinguished by the payment of the interest annually: II. Compute the interest up to the time of the first payment, and if the payment exceed the interest, deduct the excess from the principal, and cast the interest on the remainder up to the second payment, and so on. If the payment be less than the interest, place it by itself, and cast the interest up to the next payment, and so on till , the payments exceed the interests, then deduct the excess from the principal, and proceed as be. fore. By this method the interest is supposed to be always due whenever a paymeut is made; and although, on that account, it is not always perfect.y correct, it is perhaps sufficiently so for common use. This inethod is ex. tonsively used, and is established by law in Massachusetts. III. "If the contract be for the payment of interest annually, the interest becomes due at the end of each year, and if it be not extinguished by pay: ment, interest is to be cast upon that interest, from the time it becomes due up to the time of payment. If the contract be for a sum payable at a specified time, no interest is due till the time of payment arrives, and en. dorsements made before that time, are to be applied exclusively to the principal. After the debt falls due, the interest is to be extinguished an. Qually, if the payments are sufficient for that purpose. These lastiare the principles upon which interest is allowed by the courts of law in Vermont, and upon these are founded the two following rules : RULE I. When the contract is for the payment of interest annually, and no payments have been made, find the interest of the principal for each year, separately, up to the time of payment; then find the interest of these interests, seyerally, from the time they become due, up to the time of payment, and the sum of all the interests added to the principal will be the amount: but if payments have been made, find the amount of the principal, and also the amount of the payments to the end of the first year; subtract the latter amount from the former, and the remainder will be the principal for the second year; proceed in the same way from year to year up to the time of payment. NOTE.-It will sometimes happen that, when a note has endorsements, there will be years in which no payments are made ; for which years thé interest is to be found by the formerpart of the rule; and also when the amount of the payment is less than the interest of the principal, subtract the amount from that interest, and find the amount of the remainder up to the final payment. « QUESTIONS FOR PRACTICE. 1. A's note to B for 100 dollars, with interest annually, at 6 per cent. was dated January 1, 1820 ;. what was due, principal, and interest, January 1, 1824 ? 1st year, $100X.06586. Int. 1 100X.06—6 " 6X118=1.08 At the end of the first 3 100X.06= 6 " 6X.125.72 year, one year's interest, 100X.06– 6 " 6X.065.36 = dollars, is due, but as it is not paid, it draws inPrincipal, 100. 24 Int. $2.16 Int. terest for the three follow[ut. of prin. 24. ing years $1.08. Ad the Lot, of int. 2.16 end of the second year, an year's erest is Amount, $126.16 'Ans. due, which draws interest for two years; and so on. %. B's note: to C for 50 dollars, with interest annually, was dated Nov. - 20, 1822, on the back of which were ine following endorsements, viz. May 20, 1823, received 14 dollars, and Feb. 26, 1824, 30 dollars; what was change Jan. 2, 1825 ? Prin $50 Pay't. $14 Prin. $38.58 Pay't. $30 .06 .03 1.06 :0 44 Prin. 9.374 007 Am't. 53 'Abol. 14.412 Am't. 40.894 1.320 30. :067018 9.674 Am't. 31.320 Ans. $9.641 due Jan. 2, 1909 14.42 31.320 priu. 38.68 3d prin. 9.374 3. D's note to E for $1000, 4. C's note to D for 200 dolwith interest annually, was das / lars, with interest annually, ted May 5, 1822, on which the was dated June 15, 1821, on following payments were made, 1 the back of which was endorsviz. Noy. 17, 1822, 300 dollars; | ed, Sept. 15, 1821, 4 dollars, April, 23, 1823, 50 dollars, and and Jan. 21, 1823, 15 dollars: August 11, 1823, 520 dollars : what was due June 15, 1824? what was due June 5, 1824 ? Ans. $217.224. Ans. $201.713. RULE II. When the contract is for a sum payable at a specified time, with interest, and payments are made before the debt becomes due ; find the interest of the principal up to the first payment, and set it aside ; subtract the payment from the principal, and find the interest of the remainder up to the next payment, which interest set aside with the former, and so on up to the time the debt becomes due; and the sum of the interests added to the last principal, will be the amount due at that time; after the debt falls due, the interest is to be extinguished annually, if the payments are sufficient for that purpose. QUESTIONS FOR PRACTICE. year, mo. days, pay't. 25.25 lst time 12 7.06 7.06 int's, 1823 0 13 Ans, $57,06 2. F gave his note to G for 3. G's note of $365.37 was 5000 dollars, with interest, da- dated December 3, 1817, pay. ted Sept. 1, 1820, and payable | able Sept. 11, 1820 ; June 7, Jan. 1, 1824 { on the 18th of | 1820, he paid 97 dolla. 16 cts.; June, 1822, he paid 2500 dolls., what was due when the time and Aug. 25, 1823, 2500 dolls. of payment arrived ? more: what was due when the Ans. $327. 47. fume of payment arrived ? Ans. $717 082 179, 180. PER CENT. 67 Compound Unterest. 179. What will be the interest of $40 for 3 years, at 6 per cent., the interest being added to the principal at the end of each year ? The interest of 40 dollars for 1 year is (40X.063) $2.40, and $2.40+ 40.= $42.40, the principal for the second year, the interest of which is (42.40X.063) $2.544 for the second year, and $2.544+42.40=$44.944, the principal for the third year, the interest of which is (44.944X.06=) $2.696, and $2.696+44.944 $47.64, the amount of principal and interesi at the end of three years, from which subtracting 40 dollars, the first principal, we have (47.64_40=) $7.64 for the interest of 40 dollars for years.' Interest computed upon interest, as above, is called Compound Interest. 180. COMPOUND INTEREST is that which arises from making the interest a part of the principal at the end of each year, or stated time for the interest to become due. RULE. Find the amount of the given principal for the first year, or up to the first stated time for the interest to become due, by simple interest, and make the amount the principal for the next year, or stated period; and so on to the last. From the last amount subtract the given principal, and the remainder will be the compound interest required. QUESTIONS FOR PRACTICE. 1. What iş the compound 2. What is the compound interest of $125 for 2 years interest of $100 for 4 years, at and 6 months, at 6 per cent. ? 6 per cent. Ans. $26.247. $125. principal. 3. What is the compound .06 rate. interest of $200 for 1 year, at 7.50 int. for 1st. yr. months ? 6 per cent., due every four Ans. $12.241. 125. prin. added. 4. What is the amount of 132.50 am't, for 1 yr. $236 at 6 per cent., compound .06 interest, for 3 years, 5 months, and 6 days? Ans. $288.387. 7.9500 int. for 2d yr. 5. What is the amount of 132.50 prin, added. $150 at 6 per cent., compound interest, for 2 years, the inter140.45 am't, for 2d yr. est becoming due at the end .03 of Ans. $168.826. 4.2135 int. for 6 mo. 6. What is the compound 140.45 principal add. interest of $768 for 4 years, at 6 per cent : Ans. $201.58. 144.6635 am't. for 2 yrs. 7. What is the compound 125. 1st prin. sub. interest of $560 for 3 years and 6 months, at 6 per cent. ? $19.663 com. int, required. Ans. $126.977, 3. Discount. sum. 181. A holds a note against B for $218, payable in one year and six months without interest, which he wishes to turn out to B in payment for a farm; what is the present worth of the note, supposing the use of money to be worth 6 per cent. per annum ? As the amount of 1 dollar for 1 year and 6 months, at 6 per cent. is $1.09, 1 dollar is evidently the present worth of $1.09 due 1 year and o nonths hence, without interest; because, if 1 dollar be put to interest ai the above rate, at the end of 1 year and 6: months, the amount will be just sufficient to pay the $1.09. Now, as one dollar is the present worth of $1.09, due 18 months hence, the present worth of any other sum, at the same rate and for the same time, is evidently as many dollars as the number of times that sum contains $1.09. Hence to find the present worth of $218, due 18 months hence, we divide 8218 by 81.09, and the quotient (218; 1.09=) $200 is the present worth. If we subtract the present worth from ihe amount of the note, the difference, (218–2005) $18, is called the discount. The interest of the given sum for the above time and rate, would have been $19,6%, greater ihan the discount-by $1.62. DISCOUNT 182. Is an allowance made for the payment of money before it is due, or so much per cent. to be deducted from a given The present worth of a sum of money due some time kence, and not on interest, is such a sum as would, if put to interest, at a given rate, at the end of the given time, just amount to the sum then due. RULE. 183. Divide the given sum by the amount of 1 dollar for the given time and rate, and the quotient will be its present worth. Subtract the present worth from the given sum, and the remainder will be the discount. QUESTIONS FOR PRACTICE. 2. What is the present worth | at 6 per cent. per ann.: how of $125, due 3 years hence, much ready money must they discounting at the rate of 6| pay? Ans. $1047.047. per cent. per annum? 5. What is the present worth Ans. $105.93243. of $150, payable in 3 months, 3. What is the present worth discount 5 per cent:? of $376.25, due at the end of 1 Ans. $148.148. year and 6. mos., discounting 6. What is the discount upon at 5 per cent? Ans. $350. $560, due 9 months hence, at 4. A minister settled with a 8 per cent.? salary of $300 a year: wishing Ans. $31.698,5 to build a house, his parishion- 7. What is the discount of ers agreed to pay him 4 years $50, due 2 years hence, at 18 mulary in advance, discounting per cent? Ans. $9.67& |