Hence the RULE. To find the Bank Discount: Compute simple interest on the given sum for the time it is to remain on interest, plus three days of grace. To find the avails: Subtract the discount from the given sum. NOTE. Suppose the above (Ill. Ex.) was a 6 months note dated Jan. 5, which was to be discounted at a bank March 5, the operation would be precisely the same; the note would mature† July 5, with grace, July 8, and would be discounted for the time to elapse between March 5 and July 8, which is 4 months and 3 days. Find the bank discount 1. On $75 for 30 days. EXAMPLES. Ans. $.412+. 2. On a 90 days note for $500, dated May 10, and discounted June 9. (Discount for days.) Ans. $5.25. 3. On a 60 days note for $256.84, dated Oct. 28, and discounted Nov. 12. 4. On $1000 for 3 mo. at 7%. Ans. $2.054+. Ans. $18.083+. 5. What are the avails of a note of $700, discounted at a bank for 69 days? Ans. $691.60. 6. A trader buys 900 pairs of shoes at $.75 a pair cash, and immediately sells them at $.90 on a note payable in 4 months without interest; suppose he gets his note discounted at a bank for the 4 months, what will he have made? Ans. $118.395. For Dictation Exercises, see Key. 293. TO FIND FOR WHAT A NOTE MUST BE GIVEN, WHICH, DISCOUNTED AT A BANK, WILL YIELD A CERTAIN SUM. ILL. Ex. What must be the face of that note which, being discounted at a bank for 60 days, will yield $148.425? The bank discount of $1 for 63 d. : $.0105; $1 $.0105 $.9895, avails of $1. $148.425 - $.9895 $150, face of note. If $1 were discounted at a bank, it would yield $.9895; to yield $148.42, the note must be given for as many dollars as $.9895 is contained times in $148.425, which is 150 times. † See Art. 272, also Appendix, p. 330. Ans. $150. Hence the RULE. To find the face of a note which, discounted at a bank, will yield a certain sum: Divide the required sum by $1, minus the bank discount of $1 for the given time at the given rate, and the quotient will be the face of the note. EXAMPLES. 1. What must be the face of a note that it may yield $80 when discounted at a bank for 30 days? Ans. $80.442+. 2. For what must a note on 4 months, without interest, be given, that, when discounted at a bank, it may yield $489.75? Ans. $500. 3. For what must a note be given, which is to run 90 days, that it may yield $400? 4. What must be the face of a note having 60 days to run, that it may yield $989.50? 5. For what must a note, dated Sept. 1, on 4 months, be given to yield at its date $400, when interest is 7%? 6. For what must a note, dated Jan. 1, payable in 3 months, discount being 51%, be given, to yield $150? Ans. $152.162—; 7. For what must a note on 6 months be written, to yield $495.85, when the discount is 74%? For Dictation Exercises, see Key. 294. MISCELLANEOUS EXAMPLES IN BANKING, &c. NOTE. All examples in Present Worth or Discount should be considered in True Present Worth or Discount (page 202), unless Bank Present Worth or Bank Discount is definitely stated. 1. A note for $500, dated July 1, is given for 20 days without interest; what is its true value July 15? 2. What will discharge the above, Aug. 14? $200. Ans. $499.50+. (Exact days.) Ans. $502. BOSTON, April 1, 1862. Four months from date, I promise to pay JOHN BILLS, or order two hundred dollars, value received. JOHN ORNE, Jr. 3. Suppose the above to be a good and true note, what is it really worth to the holder in cash at its date, money being 6% ? Ans. $196.078+. 4. What could he get from a bank for it at its date? Ans. $195.90. 5. What would he get for it May 1, by true discount? (Art. Ans. $197.044+. Ans. $208. 287.) 6. What ought he to get for it April 1, 1863? 7. What is the difference between the avails of a note for $200, payable without interest in 18 months, whether it be paid by true or by bank discount? Ans. $1.586+. 8. What will be the difference between the true and the bank discount of a note for $90.50, due Feb. 9, 1862, and discounted June 15, 1861? Ans. $.177+. $300. HARTFORD, July 15, 1860. Six months after date, I promise to pay to the order of Cyrus Ingraham three hundred dollars. Value received. JOHN A. ANDREW. 9. What sum will the holder of the above receive, if it be discounted at a bank Sept. 15, 1860? 10. What sum would the holder of the above receive at its date by true discount? 11. What would discharge the above note May 8, 1861? 12. What would be the bank discount of the above at its date? $500. NEW BEDFORD, Oct. 5, 1860. For value received, I promise to pay Alvin Dow, or order, five hundred dollars in three months. ALLEN JONES. 13. What cash must be paid to discharge the above note at its date by true present worth? 14. What would be the avails of it at a bank Dec. 5, 1860? 15. What would be its real cash value March 17, 1861? 16. What would be the true discount on it Nov. 5, 1860? 17. What would be the bank discount of it Nov. 5, 1860? 18 What would be due on the above note Feb. 15, 1862, if $50 had been paid on it at the termination of each six months from its date, interest being 5%? 295. GENERAL REVIEW, No. 6. 1. Reduce 75%, 16%, 371%, 95%, and 831% to their lowest terms, and give their sum in a common fraction. 2. If you buy socks at $4.80 per dozen pairs, and sell at $.50 per pair, what % do you gain? 3. For what must apples which cost $1.25 per bbl. be sold to gain 20% ? 4. If 25% is lost by selling a pair of boots at $41, what was the cost? 5. What is the simple interest of $300 from May 5, 1860, to Feb. 2, 1862, at 14% a month? 6. What is the amount at compound interest of $271.36 for 2 y. 6 m. at 6% ? 7. What is the present worth of $4508.25 for 11 days, at 6%? 8. What is the bank discount of $450 for 30 days, at 5%? 9. What are the avails of a note of $100 discounted at a bank for 27 days? 10. What is the amount at simple interest of 5£. 4s. 6d. for 2 years, at 5% ? 11. The interest of $400 for a certain time at 6% was $60; what was the time? 12. What principal at 5% will gain $4.50 in 10 months? 13. At what % will $462 gain $103.95 in 2 y. 3 m. ? 14. For what must a note be given, which, discounted at a bank at 6 % for 60 days, will yield $1295? 15. Given a note for $2500, dated Sept. 5, 1862, on which were paid $50 Jan. 29, 1863, $500 July 1, 1864. The note being on interest at 6% from its date, what was due Sept. 5, 1864? For changes, see Key. COMMISSION, BROKERAGE, AND STOCKS. 296. Commission is a certain percentage received by a commission merchant for transacting business as factor, or agent, for another. 297. Brokerage is the percentage received by a broker. A Broker is one who exchanges money and deals in stocks and bills of credit. 298. Stocks are Government Bonds of all kinds, and shares of the capital invested in Banks, Insurance Companies, &c. 299. When stocks and money sell for their original or nominal value, they are said to be at par; when they sell for more than their nominal value, they are said to be at an advance, above par, or at a premium; when they sell for less than their nominal value, they are said to be at a discount, or below par. 300. In Commission, the % is estimated upon the sum actually expended; in Brokerage, upon the par value, or an assumed value. ILL. EX. My agent buys a quantity of goods for $220; what is his commission at 5 %? $220 .05 $11, Ans. Or, EXAMPLES. 1. What should a commission merchant receive for selling 4750 pounds of sugar at 12 cents a pound, his commission being 1%? Ans. 5.937+. 2. A stock broker purchases for a person 8 shares of stock in a manufacturing company at $72 a share; what is his commission at 7%? 3. What is a broker's commission for negotiating a loan of $4500 at 1%? 4. Dupee & Sayles bought on account of T. Winship, 4 shares |
