177, 178, NOTES AND BONDS. 119 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 be the insurance of 738 dolls. for selling 525 dollars worth of $738x2.005=$3.69. Ans. goods? $525 X.03=$15.75. Ans. I 4. At 33 per cent. what must 2. What is the commission 1 I allow my broker for purchaon 827 dolls. and 64 cents, at sing $2525 dollars worth of 23 per cent ? goods ? Ans. $88.374. Ans. $20.691. 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: ind the amount of t of the principal up to the time of payment, and al. so 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 remain. der 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 4 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 =82.16, which goes towards paying the principal, and in this way any debt would in time be extinguished by the payment of the interest annually. il. 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 before. By this method the interest is supposed to be always due whenever a payment is made; and although, on that account, it is not always perfectly correct, it is perhaps sufficiently so for common us extensively 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 payment, 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 ade before that time, are to be applied exclusively to the principal. After the debt falls due, the interest is to be extinguished annually, if the payments are sufficient for that purpose. These last are the principles upon which interest is allowed by the courts of law in Vermont, and upon these are founded the two following rules : RULE 1. When the contract is for the payment of interest anmually, 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, severally, 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 princi. pal, 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 ia the same way from year to year up to the time of payment. Note.-It will sometimes happen that, when a note has endorsemenis. there will be years in which no payments are made; for which years the interest is to be found by the former part 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 fiod 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 Jan. 1, 1820 ; what was due, principal and interest, Jan. 1, 1824? 1st year. $100x<.06=96 Int. 1 " 100x.06= 6 " 6x<18=1.08 At the end of the first 3 " 100*.06= 6 “ 6.125.7% year, one year's interest, 4 " 100x.06= 6 " 6x.063.36 =6 dollars, is due, but as it is not paid, it draws inPrincipal 100. $24 Int, 82.16 Int. terest for the three followInt. of prin. 24. ing years=$1.08. At the Int. of int. 2.16 end of the second year, another year's interest is due, which draw's interest Amount $126.16 Ans. for two years; and so on. 2. B's note to C for 50 dollars, with interest annually, was dated Nov. 20, 1822, on the back of which were the following endorsements, viz. May 20, 1823, received 14 dollars, and Feb. 26, 1824, 30 dollars; what was due Jan. 2, 1825 ? - Prin. $50 Pay'ı. $14 Prin. $38.58 Pay's. $30 .06 .03 .06 .007 Int. 3.00 .42 1.320 .067018 9.574 Am't. 53 Am't. 14.42 Am's. 40.894 Ala't.31.320 14.42 31.320 Ans. $9.641 due Jan. 2, 1825. 2 prin. 38.58 3d prin. 9.574 i 50 178. NOTES AND BONDS. 121 3. D's note to E for $1000, 1. 4. C's note to D for 200 dol. with interest annually, was da- lars, with interest annually, ted May 5, 1822, on which the was dated June 15, 1821, on following payments were made, i the back of which was endorsviz. Nov, 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. 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 aaDually, if the payments are sufficient for that purpose. QUESTIONS FOR PRACTICE. year. mo. days. pay't. 25.25 7.06 1824 4 1 7.06 int's. 1823 0 13 Ans. $57.06 2d time 1 3 18 2. F gave his note to G. for 1 3. G's note of $365.37 was 5000 dollars, with interest, da- dated Dec. 3, 1817, payable ted Sept. 1, 1820, and payable Sept. 11, 1820 ;-June 7, 1820, Jan. 1, 1824 ; on the 18th of he paid 97 dolls. 16 cts.; what June, 1822 he paid 2500 dolls. was due when the time of pay. and Aug. 25, 1823, 2500 dolls. / ment arrived ? . more; what was due when the i , Ans. 327 dolls. 46 cts, time of payment arrived ? Ans. $717.082. Conypound Enterest. 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.06=) $2.40, and $2.40 40.=$42.40, tle principal for the second year, the interest of which is (42.40X.06=) $2.344 for the second year, and $2.544+-42.40=$44.944 the principal for the third year, the interest of which is (44.944 ,06=5 $2.696, and $2.696-7 44.944=$47.64, the amount of principal and interest at the end of three years, from which subtracting 40 dollars, the first principai, we have (47.64--40.=) $7.64 for the 'interest of 40 dollars for 3 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. RUJE 1. 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 is the compound in 1 2. What is the compound terest of $125 for 2 years and interest of $100 for 4 years, at 6 months, at 6 per cent.? 16 per cent? Ans. $26.247. $125. principal. 1 3. What is the compound .06 rate. interest of $200 for 1 year, at 6 per cent, due every four 7.50 int. for 1st yr. 1 months ?. Ans. $12.241.. 125. prin. added. I 4. What is the amount of $236 at 6 per cent, compound 132.50 amt. for 1 yr. I interest, for 3 years, 5 months, .06 and 6 days? Ans. $288.387. 7.9500 int. for 2d yr. | 5. What is the amount of 132.50 prin. added. į $150 at 6 per cent, compound interest, for 2 years, the inte140.45 amt. for 2d yr. | rest becoming due at the end of every 6 months ? 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 i 6 per cent ? Ans. $201.58. 144.6635 amt. for 2 ys. 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. 181, 182, 183. DISCOUNT. 181. A holds a note against B for $218, payable in 1 year and 6 6 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 6 months hence, without interest; because if i dollar be put to interest at the above rate, at the end of 1 year and 6 nionths, the amount will be just sufficient to pay the $1.09. Now as 1 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 num ber of tinies that sum contains $1.09. Hence to find the present worth of $218, due 18 months hence, we divide $218 by $1.09, and the quotient (218–1.09=) $200 is the present worth. If we subtract the present worth from the amount of the note, the difference, (218–2005) $18, is call the discount. The interest of the given sum for the above time and rate, would have been $19.62, greater than the discount by $1.62. DISCOUNT 182. Is an allowance made for the payment of of money before it is due, or so much per cent to be deducted from a given sum. The present worth of a sum of money due some time hence, 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 tiine 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. $1047.04. per cent per annum ? 1 5. Wbat is the present worth Ans. 8105.9321. I 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 . Aps. $148.148. year and 6 months, 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. $31.66941 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 12 salary in advance, discounting / per cent ? .. Ans. $9.678. |