pay Joseph Trotter, or order, Five Thousand Four Hun dred and Eighty Dollars, without defalcation. JAMES TAYLOR. Indorsements: March 15, $200; June 12, $300; Aug. 9, $500; Oct. 1 $700. What is due Dec. 3, 1875? Ans. $3997.60. 2. A note of $4774.25 was given Nov. 9, 1875. Indorsements: Jan. 1, 1876, $500; Feb. 12, $600; April 17, $450; June 10, $247.50; Aug. 1, $250. What is due Oct. 1, 1876, at 7% ? Ans. $2953.592. 3. A note was given for $1250, April 20, 1874. Indorsements: May 10, $200; July 17, $50; Sept. 25, $140; Oct. 19 $150; Dec. 12, $350. What was due April 20, 1875, at 5%? Ans. $396.89. NOTE.-For Connecticut, Vermont, and New Hampshire rules, see Brooks's Higher Arithmetic. DISCOUNT AND PRESENT WORTH. 494. Discount is an allowance made for the payment of money before it becomes due. 495. The Present Worth of a debt payable at a future time without interest is such a sum as, being on interest for the time at a certain rate, will amount to the debt. 496. The True Discount is the difference between the amount of the debt and the present worth. NOTES.-1. The true discount is the interest on the present worth for the time between the payment of the debt and the time it becomes due. 2. The present worth corresponds to the principal, the discount to the interest, and the debt to the amount; hence the different cases may be solved as in Interest. OPERATION. 1. What is the present worth of $585, due 5 years hence without interest, money being worth 6% ? SOLUTION.-The amount of $1 for 5 years, at 6%, is $1.30, hence the present worth of $1.30 is $1, and the present worth of $585 is as many times $1 as $1.30 is contained times in $585, which is $450. Hence $0.06×5 $0.30 Amount $1.30 $585÷1.30 $450, Ans, Rule.-I. Divide the given sum by the amount of $1 for the given rate and time, to find the present worth. I Subtract the present worth from the given sum to find the discount. NOTE.-When several payments are made without interest, find the present worth of each separately, and take their sum. WRITTEN EXERCISES. 2. What is the present worth of $1206, due 5 yr. 8 mo. hence without interest, money worth 6% ? Ans. $900. 3. What is the discount of $6460, due 4 yr. 10 mo. 12 da. bence without interest, money worth 6%? Ans. $1460. 4. A owes $2178 payable in 3 yr. 9 mo. without interest, but wishing to pay it immediately, what should he in equity pay, money worth 7 per cent.? Ans. $1725.14+. 5. B bought $2500 worth of goods on 6 mo. 18 da. credit; what allowance should be made, if the bill be paid immediately, money being worth 6%? Ans. $79.87-. 6. I can sell my horse for $280 cash or $300 on 1 yr. 6 mo. credit; I choose the latter; how much did I lose, money being worth 6 per cent.? Ans. $4.77+. SUPPLEMENTARY PROBLEMS. To be omitted unless otherwise directed. 7. A gives his note for $850 payable in 2 yr. 8 mo. without interest; at the end of 8 mo. he wishes to pay the note; what should the holder of the note receive? Ans. $758.93—. 8. A man owes $600, of which one-third is to be paid in one year and the remainder in two years; what is the present value of the note, money worth 6 per cent ? Ans. $545.82. 9. What is the present worth of $2400, one-fourth due in 8 mo., one-third in 1 year, and the remainder in 18 mo., money being worth 6 per cent? Ans. $2249.07. BANK DISCOUNT AND BANKING. 497. A Bank is an incorporated institution which receives and loans money, or furnishes a paper circulation. 498. A Bank of Deposit is one which receives money or its equivalent on deposit, to be drawn at the order of the depositor. 499. A Bank of Discount is one that lends money, discounts notes, drafts, etc. A Bank of Issue is one that makes and issues notes to circulate as money. Some banks unite two and some all of these offices. A Savings Bank is one that receives small sums on deposit, and pays interest to its depos 500. A Check is an order on a bank, given by one of its depositors, to pay a certain amount to some person or his order, or to bearer. 501. Bank Discount is the interest on the face of the note for the time from the day of discount to the day of · payment. 502. The Proceeds or Avails of a note is the sum received for it when discounted. It equals the face or amount of the note less the discount. 503. The Term of Discount is the number of days from the time of discounting to the time of maturity of the note. When a person wishes to borrow money at a bank, he presents a note, either made or indorsed by himself, payable at a certain time, and receives for it a sum equal to the face less the interest for the time the note has to run. This amount is withheld by the bank in consideration of advancing money on the note prior to its maturity. In Pennsylvania, Delaware, Maryland, Missouri, and the District of Columbia, the day of discount and day of payment are both reckoned. A 60-day note in Pennsylvania would be discounted for 61 days; in the others named (grace being allowed) for 64 days. Business men often discount notes by deducting the interest for a given time, with or without grace, as may be agreed upon. The rate is fixed by agreement, and may be other than the legal rate. 504. The difference between bank discount and true discount may be shown as follows: If I take my note to the bank promising to pay $106 at the end of 1 year, to get it cashed, by the method of true discount I would receive $100; but by the method of bank discount, not counting days of grace, I would receive $106 minus the interest of $106 for 1 year, that is, $106 -$6.36 $99.64. CASE I. 505. Given, the face of the note, the rate, and the time, to find the discount and the proceeds. 1. What is the present worth or proceeds of a note for $600, due in 21 days, discounted at a bank at 6 per cent. ? SOLUTION. We find the interest of $600 for 21 da. is $2.10, which is the discount. Subtracting this from $600, we have the proceeds, equal to $597.90. OPERATION. $600 21÷6=.0035. .0035 $2.1000 $597.90. Ans. Rule. I. Find the interest on the face of the note for the time and rate, for the discount. II. Subtract the discount from the face, to find the present worth. NOTE.-The discount of an interest-bearing note is computed on the amount of the note at its maturity. Banks compute interest for the actual number of days a note has to run, whether a note is drawn for months or days. NOTE. In the problems in this and the following cases, marked with a star, grace is allowed. WRITTEN EXERCISES. 2. A note for $275, due in 60 days, was discounted at a bank at 7%; what was the discount? Ans. $3.21-. 3. A note for $965, at 90 days, was discounted at 7%; required the proceeds. Ans. $948.11. 4. A note, for $876.50, due in 60 days, was discounted by a bank at 6%; required the proceeds. Ans. $867.74. 5. Required the difference between the true discount and the bank discount of $690, due in 2 yr. 6 mo., money worth 6%, not reckoning days of grace. Ans. $13.50. Find the discount and proceeds of the following notes: PHILADELPHIA, March 16, 1870. 6. $650 25% 100 Four months after date I promise to pay Thomas Newman, or order, Six Hundred and Fifty 25 Dollars, at the Girard Bank, value received, without defalcation. HENRY OSBORN. Discounted, April 1st, 1870, at 6%. Ans. Dis., $11.60. *7.$135,5%. WASHINGTON, Aug. 20, 1872. Three months after date, for value received, I promise to pay W. H. Seal, or order, One Hundred Thirty-five Dollars, without defalcation. D. NEWLIN FELL. Discounted, Sept. 7, 1872, at 6%. Ans. Discount, $1.76. 8. $750. CHICAGO, June 16, 1876. Nine months after date, for value received, I promise to pay Mary Smith, or order, Seven Hundred Fifty Dollars with interest, at 6 per cent. FANNIE E. WILLARD Discounted, at 6%, Oct. 24, 1876. Ans. Dis., $18.69. NOTE.-In Ex. 6, the time is 106+1=107 da.; in Ex. 7, it is 74+4=78 da., in Ex. 8, it is 143 da., see note under Art. 503. CASE II. 506. Given, the rate, the time, and the proceeds or the discount, to find the face. 1. I wish to borrow $800 from a bank; for what must I give my note at 30 days, discounting at 6 per cent.? SOLUTION.-We find the interest of $1 for 30 days and subtract it from $1, which gives the proceeds of $1. If for every $1 in the face of the note the proceeds are $0.9945, to give $800 proceeds will require as many times one dollar as $0.9945 is contained times in $800, which are $804.02. OPERATION. $1.000 .995, Proceeds of $1. 800 .995 $804.02+. Rule.-Divide the given proceeds by the proceeds of $1 for the given time and rate; or divide the discount by the discount of $1. WRITTEN EXERCISES. 2. A wishes to borrow $1000 from a bank for 60 days; for what sum must he give his note, discounting at 6 per cent. ? Ans. $1010.10. 3. What is the face of a note at 90 days, the proceeds of which, discounted at 6%, are $2000? Ans. $2030.46. 4. For what sum must a note be drawn at 60 days to net $5000, when discounted at 6 per cent.? Ans. $5050.51 5. A broker buys a 60 day note for $20 less than the face; what was the face, discount 6 per cent.? Ans. $2000. SUFPLEMENTARY PROBLEMS. To be omitted unless otherwise directed. 6. Find the face of a 6 mo. note which, when discounted at 1 per cent. a month, yields $686.20. Ans. $730. 7. Owing $1000, I gave a 90 day note, which was discounted at 14% a month; required the face of the note? Ans. $1038.96. *8. Mr. Schofield presented a 30 day note at a Baltimore bank for discount; the proceeds were $954.56; what was the face of the note, (the day of discount included)? Ans. $960. CASE III. 507. Given, the face, the rate, and the proceeds w the discount, to find the time. 1. The proceeds of a note for $600, discounted at €%, ar $594.00; what was the time? |