(3.) $2400. New York, May 16, 1864. For value received, I promise to pay J. L. Weston and Company, or order, on demand, twenty-four hundred dollars, with interest after three months. J. M. Meigs. [Stamp.] INDORSEMENTS. August 16, 1865, $400; May 31, 1866, $67.89. How much was due November 30, 1866, interest at 7 % ? Ans. $2295.71. New Orleans, May 1, 1863. (4.) $5660. For value received, I promise to pay to the order of Louis De Bois five thousand six hundred and sixty dollars, on demand, with interest. John Vincent. [Stamp.] INDORSEMENTS. June 16, 1864, $5783; Jan. 31, 1865, $160; June 16, 1866, $420. How much was due February 16, 1867, interest at 5% ? Ans. $5538.71. 315.* The preceding rule modified, so as not to allow of computing interest between payments for any period less than a year, is the CONNECTICUT RULE. When at least a year's interest has accrued at the time of a payment, and also in case of the last payment, proceed according to the United States Rule. When less than a year's interest has accrued at the time of any payment, except the last, take the difference between the amount of the principal for a whole year, and the amount of the payment for the remainder of the year after it was made, for a new principal. When the interest which has accrued at the time of a payment exceeds the payment, find the interest only upon the principal. REVIEW QUESTIONS. What is the General Rule for computing simple interest? (294) The Rule for interest at 6 per cent.? (295) (1.) $1000. New Haven, July 1, 1864. For value received, I promise to pay to the order of H. B. Bacon, one thousand dollars, on demand, with interest. [Stamp.] INDORSEMENTS. Richard Russell. January 1, 1865, $100; September 1, 1866, $223.99; December 25, 1866, $12. How much was due January 1, 1867 ? Ans. $804. 316.* The General Assembly of Vermont, in 1866, by law, established the following as the VERMONT RULE. On all notes, bills, or other similar obligations, whether made payable on demand or at a specified time, WITH INTEREST, where payments are made, such payments shall be applied: first, to liquidate the interest that has accrued at the time of such payments; and, secondly, to the extinguishment of the principal. On all notes, bills, or other similar obligations, whether made payable on demand or at a specified time, WITH INTEREST ANNUALLY, the annual interests that remain unpaid shall be subject to simple interest, from the time they become due to the time of final settlement; but if in any year reckoning from the time such annual interest began to accrue, payments have been made, the amount of such payments at the end of such year with interest thereon from the time of payment shall be applied: first, to liquidate the simple interest that has accrued from the unpaid annual interests; secondly, to liquidate the annual interests that have become due; and thirdly, to the extinguishment of the principal. Examples. (1.) $5000. Montpelier, Vt., Dec. 1, 1867. For value received, we promise to pay to the order of James Mason, five thousand dollars, on demand, with interest. [Stamp.] Richardson, Bentley & Co. INDORSEMENTS. June 1, 1869, $400; December 1, 1869, $2200. What was due June 1, 1870? (2.) $1000. Ans. $3090 Pomfret, Vt., Oct. 1, 1862. For value received, I promise to pay Andrew Baldwin, or order, one thousand dollars, three years from date, with interest annually. Charles Dayton. INDORSEMENTS. April 1, 1864, $50; June 1, 1865, $400; August 1, 1865, $200. What was due at maturity? COMPOUND INTEREST. Ans. $526.43. 317. Compound Interest is interest upon principal and interest, the two being combined at regular intervals of time and converted into a new principal. The interest may be made a part of the principal, or compounded, annually, semi-annually, quarterly, etc., according to agreement. 318. To find the compound interest of any sum. 1. What is the compound interest of $600 for 2 years and 6 months, at 6 %? Compound interest for 2 y. and 6 mo., $94.3848 What is Compound Interest? How often may the interest be com pounded? Explain the operation. The interest for the first year is $36, and the amount $636, which is made a second principal. The interest for the second year is $38.16, and the amount, $674.16, which is made a third principal. The interest for 6 months, the time at the end of the entire years, is $20.2248, and the amount $694.3848. Subtracting the given principal from the last amount, the compound interest is $94.3848. RULE. Find the amount of the principal for the first interval, and make it the principal of the second interval; then, the amount of the second principal for the second interval, and make it the principal of the third, and so on for all the entire intervals. If there be a part of the time more than the entire intervals, find the amount for it. The last amount will be the amount at compound interest, and it, less the given principal, will be the compound interest. Examples. 2. What is the amount of $100, at 6 % compound interest, for 3 years? Ans. $119.10+. 3. What is the compound interest of $600.50, at 5 %, for 2 years? 4. What is the compound interest of $300, at 7 %, for 3 years, 4 months, and 15 days? Ans. $77.15+. 5. What is the amount of $860, at 4 % half yearly compound interest, for 3 years? Ans. $1088.17+. 6. What is the amount of $500, at 5 % compound interest, for 4 years, 2 months, and 15 days? Ans. $614.08+. 319. The process of computing compound interest may be abridged by means of the following Repeat the Rule. How may the process of computing compound interest be abridged ? Table, SHOWING THE amount of $1 FROM 1 TO 20 YEARS, AT 2, 3, 5, 6, AND 7 PER CENT., COMPOUND INTEREST. Years. 2 per cent. 3 per cent. 5 per cent. 6 per cent. 7 per cent. Years. 1 1.025000 1.030000 1.050000 1.060000 1.070000 1 2 1.050625 1.060900 1.102500 1.123600 1.144900 2 3 1.076890 1.092727 1.157625 1.191016 1.225043 3 4 1.103812 1.125508 1.215506 1.262476 1.310796 4 5 1.131408 1.159274 1.276281 1.338225 1.402552 5 6 1.159693 1.194052 1.340095 1.418519 1.500730 6 7 1.188685 1.229873 1.407100 1.503630 1.605781 7 8 1.218402 1.266770 1.477455 1.593848 1.718186 8 9 1.248862 1.304773 1.551328 1.689478 1.838459 9 10 1.280084 1.343916 1.628894 1.790847 1.967151 10 11 1.312086 1.384233 1.710339 1.898298 2.104852 11 12 1.344888 1.425760 1.795856 2.012196 2.252191 12 13 1.378511 1.468533 1.885649 2.132928 2.409845 13 14 1.412973 1.512589 1.979931 2.260903 2.578534 14 15 1.448298 1.557967 2.078928 2.396558 2.750032 15 16 1.484505 1.604706 2.182874 2.540351 2.952164 16 17 1.521618 1.652847 2.292018 2.692772 3.158815 17 18 1.559658 1.702433 2.406619 2.854339 3.379932 18 19 1.598650 1.753506 2.526950 3.025599 3.616527 19 201.638616 1.806111 | 2.653297 3.207135|3.869685 20 7. What is the compound interest of $400, at 6 %, for 20 years and 6 months? SOLUTION. Amount of $1 for 20 years $3.207135; interest of $1 for 6 months = $.03; $3.207135 × .03 = $.09621405 = interest of amount for 6 months; $3.207135 — $1 = $2.207135 compound interest of $1 for 20 years; $2.207135+ $.096214 = $2.303349 = compound interest of $1 for 20 years and 6 months; and $2.303349 X 400 = $921.3396, or $921.33+ = compound interest of $400 for 20 years and 6 months. 8. What is the amount of $100, at a semi-annual compound interest of 21%, for 10 years? Ans. $163.86+ |
