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NOTE.—When several payments are made without interest, find tho present worth of each separately, and take their sum.
WRITTEN EXERCISES. 2. What is the present worth of $1206, due 5 yr. 8 mo. bence 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, Mut wishing to pay it immediately, what should be 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 imme diately, money being worth 6%?
Ans. $79.876. 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 directe d. 7. A gives his note for $850 payable in 2 yr. 8 mo. without in. terest; 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 prescnt 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 wbich receives and loads money, or furnishes a paper circulation.
498. A Bank of Deposit is one which receives money or its equivalent on deposit, to be drawa 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 Band is one that receives small sums on deposit, and pays interest to its depos500. A Check is an order on a bank, given by one of its depositors, to pay a certain amount to some person or bis order, or to bearer.
501. Bank Discount iş 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 re. ceived 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 oj 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, thai 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 dis
$600 21:6=.0035. count. Subtracting this from $600, we .0035 have the proceeds, equal to $597.90.
Rule. - I. Find the interest on the fuce 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, wbether 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 : 6. $6502
PHILADELPHIA, Jarch 16, 1870. Four months after date I promise to pay Thomas Newman, or order, Six Hundred and Fifty 14 0 Dollars, at the Girard Bank, value received, without defalcation.
HENRY OSBORN. Discounted, April 1st, 1870, at 6%. Ans. Dis., $11.60. *7. $1356
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. %, $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.-I» 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 pote under Art. 503.
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 ior 30 days and subtract it from $1, which
$1.000 gives the proceeds of $1. If for every $1
.005 in the face of the note the proceeds are $0.9945, to give $800 proceeds will require
.995, Proceeds of $1. as many times one dollar as $0.9945 is 800 contained times in $800, which are $804.02.
.995 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 be 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.
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)?
CASE III. 507. Given, the face, the rate, and the proceeds zem the discount, to find the time.
1. The proceeds of a note for $600, discounted at 6%, % $594.00; what was tbe time?
SOLUTION.–Subtracting $594 from $600,
OPERATION. we find the discount is $6. The discount on
$600 $1.00 for one day, at 6%, is į of a mill; and 594 on $600 it is 600X$.000], or $0.10. Hence
6 discount. the note was discounted for as many days as $0.10 is contained times in $6, or 60 days.
6.005.10—60 days. Rule.-Divide the discount by the interest on the face for one day.
NOTE.-When graca is allowed, wo subtract three days from the quotient to find the time of the pole.
2. A merchant discounts a note for $2000 at a bank, and receives $1970; what is the time?
Ans. 90 days. 3. A commission merchant sold a consigoment of cotton for $4500, receiving in payment a note, which yielded, on being discounted, $4477.50; what was the time of tbe note ?
Ans. 30 days. 4. A note dated June 21st, 1875, was discounted July 1st at 7%; the face of the note was $6540 and the proceeds $6472.60; bow long had it to run after it was discounted ?
Ans. 53 days. SUPPLEMENTARY PROBLEMS.
To be omitted unless otherwise directed. *5. A note dated Jan. 15th, 1884, at 6 months, was discounted at the First National Bank, St. Louis ; the proceeds were $8402.25, aud the face $8500 ; what was the date of discount? Ans. May 11.
6. An iuterest-bearing note, dated Aug. 1, 1888, at 90 days, was discounted at 8%; the face was $750, and the proceeds $759.982 ; what was the date of discount?
Ang. Sept. 30.
508. Given, the face, the time, and the proceeds or the discount, to find the rate.
1. The proceeds of a note for $300, at 30 days, are $298.50; wbat is the rate ?