« ΠροηγούμενηΣυνέχεια »
- 73. A BANK is an incorporated institution, created for the purpose of loaning money, receiving deposites, and dealing in exchange,
The Stack, or amount of money in trade, is limited by law, and owned by various individuals, who are called stockholders.
Banks are allowed to make notes, which are denominated bank bills, which circulate as money, because they are obliged to redeem them with specie.
It is customary for banks, in most cases, when they loan money, to take the interest in advance ; that is, to deduct it from the face of the note, at the time the money is lent. The note is then said to be discounted.
The sum to be discounted, or the face of the note, is called the amount.
The interest deducted is called the discount.
A note to be discounted, or bankable, must be made paya. ble at some future time, and to the order of some person who endorses it. .
It is usual for the banks to take interest for three days more than the time specified in the note ; and the borrower is not obliged to make payment till those three days have expired, which are for this reason, called days of grace.
To find the banking discount on any sum of money, we have this.
RULE. Compute the interest (by Case III. Art. 65) on the given sum, for three days more than is specified.
Examples. 1. What is the banking discounton $1000, for three months, at 7 per cent. ? ,
In this example we find the interest on $1, for 3 months and 3 days, at 6 per cent., to be $0.0155, which, multiplied by $1000, gives $15.50, for the discount at 6 per cent. ; this, increased by its sixth part, becomes $18.083, for the discount at 7 per cent., as required. '
2. What is the banking discount of $150, for 6 months, at 6 per cent. ?
Ans. $4.575. 3. What is the banking discount of $375, for 3 months and 9 days, at ny per cent. ?
Ans. $7.438. 4. What is the banking discount of $400, for 9 months, at 7 per cent. ?
5. What is the banking discount of $29.30, for 7 months, at 5 per cent. ?
6. What is the banking discount of $472, for 10 months, at 7 per cent. ?
When the present worth of a bankable note, the time for which it is to be discounted, and the rate per cent, is given, to find the amount, we have this
RULE. Compute the banking discount on $1, for the given time and ratio, subtract this discount from $1, then divide the present worth by the remainder, and the quotient will be the amount.
Examples. 1. What must be the amount of a bankable note, so that when discounted for 3 months at 6 per cent., shall give a pres. ent worth of $600 ? -.
In this example we find the banking discount on $1, for 3 months, to be $0.0155, which, subtracted from $1, gives $0.9845; , . dividing $600 by $0.9845, we obtain $609.446, for the required amount of the note.
2. What must be the face of a bankable note, so that when discounted for 2 months, at 7 per cent., the borrower shall receive $50 ?
. Ans. $50.62. The following table gives the amount of a bankable note, so that when discounted at 5, 6, or 7 per cent., for any number of months, from 1 to 12, the present worth shall be just $1.
Months. 5 per cent. | 6 per cent. 17 per cent.
1.004604 | 1.005530 | 1.006458
1.034929 | 1.042095 | 1.049593
1.053093 1.064396 | 1.075944
We will now work some examples by the aid of the above table.
3. What must be the face of a bankable note, so that when discounted for 10 months, at 5 per cent., the present worth may be $1000 ?
Looking in the table directly under the 5 per cent., and adjacent to 10 months, we find $1.043932, this, multiplied by $1000, gives $1043.932, for the face of the note required.
4. What must be the face of a bankable note, so that when discounted for 7 months, at ny per cent., the present worth may be $70.50 ?
Ans. $73,546.. 5. What amount must I make my note, so that when dist counted at the bank for 12 months, at 7 per cent., I may re. ceive $100 ?
Ans. $107.594, 6. What must be the amount of a note, so that when discoun. ted at the bank for 6 months, at 6 per cent., the borrower may receive $365 ?
7. What must be the amount of a note, so that when discoun. ted at the bank for 9 months, at 7 per cent., the borrower may receive $500 ?'
74. The banks, by their method of discounting, obtain a larger per cent. for their money then is obtained by the usual method of loaning money. To illustrate this, suppose A gets a note of $1 discounted at the bank for 12 months, or one year, at 7 per cent., he receives $0.93; the $0.07 is re. tained by the bank, it being the interest of $1 for one year : this $0.07 may now be loaned to B, and its interest again withheld; and so on, for an indefinite period of terms; hence, at the end of the year, the bank will receive for its $1, the number of dollars expressed by the sum of the terms of the following geometrical progression :
ItintGio) + Géo) + &c., this, summed by rule un. der Art. 64, gives yo=1.0752688. Therefore in this case the bank receives 7.52688 per cent. per annum for its money.
The longer the time for which they discount, the larger per cent. do they receive.
To make this appear obvious, suppose a person wished his note discounted at the bank for 144 years, at ny per cent. ; in this case, the interest would equal the whole face of the note 80 that the bank would withhold the whole amount, be that ev. er so large, and the borrower would not receive a single cent, but would nevertheless be obliged to pay to the bank, at the end of 144 years, the face of the note. In this case the per cent. would be infinite.
If we go one step farther, and endeavor to discount a note at the bank for a longer period than 144 years, at 7 per cent., we shall be obliged to pay to the bank money from our own pocket, before they would accept our note.
The following table shows the per cent. received by banks, when their notes are renewed at the end of any number of months, from 1 to 12, at 5, 6, and 7 per cent., lawful interest.
Months. 5 per cent. 16 per cent. | 7 per cent.
5.138 6.200 7.272
5.228 6.332 7.456
5.251 6.366 17.503
NOTE. –Were it possible to renew their notes every instant, the respective rates per cent. would be 5.127, 6.182, and 7. 251. This is the same as would be received if the interest were added every instant.