Find the date when the following notes become due, the bank discount, and the proceeds: 5. $960,0% Harrisburg, Aug. 10, 1869. Three months after date, I promise to pay to the order of Geo. F. Phelps nine hundred sixty dollars, without defalcation, value received. THOMAS J. FREEMAN. The above was discounted August 26, at 7%. Ans. Nov. 10/13; $ 14.76 dis.; $ 945.91 proceeds. Chicago, Nov. 18, 1868. Sixty days after date, we promise to pay to the order of E. Staples & Co. one thousand dollars at the Fourth National Bank, Chicago, value received. WOODMAN & WADSWORTH. The above was discounted Nov. 27, at 10%. Ans. Jan. 17/20, 1869; $ 15 dis. ; $ 985 proceeds. 7. I had three $500 notes, dated severally September 1, October 1, and December 1, 1868, and payable in 6 months; these notes were discounted by a banker February 1, 1869, at 12%; what was the sum of the proceeds? Ans. $1,464. 471. TO FIND THE FACE OF A NOTE THAT SHALL YIELD A GIVEN SUM WHEN DISCOUNTED AT A BANK FOR A CERTAIN TIME AND RATE. ILL. EX. For what sum must a 60 days' note be drawn so that when it is discounted at a bank at 6% the proceeds shall be $1400 ? Explanation. The bank discount of $1 for 63 days at 6% is $.0105. The proceeds of $1 for 63 days are $1-$.0105, which is $.9895. Since $.9895 is the proceeds of $ 1, the note must be drawn for as many dollars as there are $.9895's in $1400. Ans. $1,414.86. PROOF. Interest on $1414.86 for 63 days = = $14.86, Discount. $1,400, Proceeds. From the above may be derived the following RULE. To find the face of a note that shall yield a certain sum when discounted at a bank: Divide the given sum by the proceeds of $1 for the given time and rate. EXAMPLES. 8. For what sum must a 90 days' note be drawn so that when it is discounted at a bank at 6% the proceeds shall be $ 448.932 ? Ans. $456. 9. What must be the face of a note given for 105 days, to obtain $ 244 from a bank, discount being at 8% ? Ans. $250. 10. Two notes were discounted, each for 30 days and grace; the proceeds of the first were $1243.12, the rate 6%; the proceeds of the second, $1688.78, the rate 71%; what sum will discharge both notes at maturity? Ans. $2,950. 11. For what sums must three six-months' notes be drawn, dated severally April 1, May 1, and June 1, and discounted at a bank, September 1, at 6%, that the proceeds of each may be $1600 ? Ans. $1,608.85; $1,617.25; $1,625.47. For Dictation Exercises in Banking, see Key. ANNUAL INTEREST. NOTE. Teachers of New Hampshire and Vermont will find a treatment of ANNUAL INTEREST on page 321. COMPOUND INTEREST. 472. ILLUSTRATION. - January 1, 1860, I had a deposit of $1000 in a savings bank; at the end of 6 months the deposit was increased by the interest, which was 3% of the $1000; at the end of another six months the amount thus formed was increased by the interest, which was 3% of the amount. Interest was here employed semi-annually to increase the . principal, and cach successive amount became a new principal upon which interest was computed. Interest employed to increase the principal at stated intervals is compound interest. NOTE I. Interest which is computed upon the principal only is simple interest. NOTE II. When the kind of interest is not specified, simple interest is meant. NOTE III. Interest may be compounded annually, semi-annually, quarterly, or at any specified time. 473. ILL. Ex. In the illustration above, what was the amount due at the end of the third six months? What interest had accrued ? second interval of time, and thus continue for the entire time. The last amount will be the amount at compound interest. 2. The last amount minus the given principal will be the compound interest. EXAMPLES. 1. What is the amount of $261 for 3 years at 6%, interest compounding annually? semi-annually? Ans. $310.86; $ 311.65. 2. What are the amount and interest of $2000 at 7% for 1 y. 6 m., interest compounding semi-annually? Ans. $ 2,217.44; $217.44. 3. What is the amount of $2000 for 2 y. 6 m. at 7%, interest compounding annually? NOTE.$2000 X 1.07 X 1.07 X 1.035 = $2369.94. Ans. $ 2,369.94. Ans. 375.10. 4. What is the amount of $ 340 for 1 y. 3 m. at 8%, interest compounding semi-annually? 5. What is the amount, the interest compounding quarterly? Ans. $375.39. 6. What is the interest of $789 at 6% from Nov. 17, 1866, to July 2, 1869, interest compounding annually? (Art. 337, Note I.) Ans. $130.76. 474. The process of computing compound interest may be shortened by the use of the following TABLE, Showing the amount of $1 at compound interest from 1 year to 15 years, at 3, 4, 4, 5, 6, and 7 per cent. Years. 3 per cent. 4 per cent. 4 per cent. 5 per cent. 6 per cent. 7 per cent. 1.050000 1.060000 1.070000 4 1.030000 1.040000 1.045000 1.125509 1.169859 1.192519 1.215506 1.262477 1.310796 5 1.159274 1.216653 1.246182 1.276282 1.338226 1.402552 6 1.194052 1.265319 1.302260 | 1.340096 1.418519 1.500730 7 1.229874 1.315932 1.360862 1.407100 1.503630 1.605781 829 1.266770 1.368569 1.422101 1.477455 1.593848 1.718186 1.304773 1.423312 1.486095 1.551328 1.689479 1.838459 10 1.343916 1.480244 1.552969 1.628895 1.790848 1.967151 11 1.384234 1.539454 1.622853 1.710339 1.898299 2.104852 12 1.425761 1.601032 1.695881 1.795856 2.012197 2.252192 13 1.468534 1.665073 1.772196 1.885649 2.132928 2.409845 14 1.512590 1.731676 1.851945 1.979932 2.260904 2.578534 15 1.557967 1.800943 1.935282 2.078928 2.396558 2.759031 ILL. Ex. At 6% compound interest for 3 y. 5 m., what is the amount of $200? What is the compound interest of $200 ? Explanation. We find by the table the amount of $1 for 3 years to be $1.191016. We next find the amount of $1.191016 for 5 months, which is $ 1.220791, which equals the amount of $1 for 3 y. 5 m. Multiplying $1.220791 by 200 we obtain for the amount of $200, $244.158, 1st Ans. Having found the amount, we can obtain the interest by taking the difference between the amount and principal, or it can be obtained by multiplying .220791, the interest of $1 for 3 y. 5 m., by 200. 2d Ans. $ 44.158. EXAMPLES. Interest compounding annually, find, by the use of the above table, the interest 7. Of $860 for 5 y. at 6%. 8. Of $300 for 13 y. 3 m. at 5%. 9. Of $400 for 25 y. at 6%. Ans. $290.87. Ans. $272.77. NOTE.- Find by the table the amount of $ 400 for 15 years, then find the amount of this amount for 10 years. Ans. $1,316.75. 10. Interest compounding semi-annually, what is the amount of $3500 for 7 years at 6%? NOTE. The interest on the above compounds 13 times at 3%; hence we take from the table the amount of $1 for 14 years at 3% and multiply it by $500. Ans. $5,294.07. Interest compounding semi-annually, what is the amount 11. Of $480 for 6 y. at 9%? at 8% ? 1st Ans. $814.02. 12. Of $357.60 for 4 y. 6 m. at 10%? at 6%? 1st Ans. $554.75. PARTIAL PAYMENTS. 475. ILLUSTRATION. A note was given for $1500 Sept. 1, 1865, payable on demand with interest at 6%; to discharge the interest and in part pay the note, payments were made as follows: September 1, 1866, $ 500. March 1, 1867, $ 122.70. September 1, 1867, $ 25. 476. Payments in part of a note or other debt are called partial payments. 477. A record of the amount of each payment, with its date, is made upon the back of the note; such a record is an indorsement. 478. ILL. Ex. If the above note was settled September 1, 1868, what was the balance due? |