CHAPTER VIII. BANKING. 72. A BANK is an incorporated institution, created for the purpose of loaning money, receiving deposits, and dealing in exchange. The Stock, 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. What remains is called the present worth, or proceeds. A note to be discounted, or bankable, must be made payable at some future time, and to the order of some person who indorses 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 * This method of discounting bank notes is usurious, and is fast going out of use, and instead thereof the banks now deduct the discount as found by rule under Art. 66. 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. 63,) on the given sum for three days more than is specified. EXAMPLES. 1. What is the banking discount on $1000 for 3 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 $18.08 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 7 per cent.? Ans. $7.438. 4. What is the banking discount of $400 for 9 months, at 7 per cent.? Ans. $21.233. 5. What is the banking discount of $29.30 for 7 months, at 5 per cent.? Ans. $0-867. 6. What is the banking discount of $472 for 10 months, at 7 per cent.? Ans. $27.808. When the present worth of a bankable note, the time. for which it is to be discontinued, 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 rate per cent.; subtract this discount from $1, then divide the present worth by the remainder, and the quotient will be the number of dollars in the amount. EXAMPLES. 1. What must be the amount of a bankable note, so that, when discounted for 3 months, at 6 per cent., it shall give a present 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 number of dollars in 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. We will now work some examples by the aid of the preceding 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 $1043932; 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 7 per cent., the present worth may be $70.50? Ans. $73546. 5. What amount must I make my note, so that, when discounted at the bank for 12 months, at 7 per cent., I may receive $100? Ans. $107.594. 6. What must be the amount of a note, so that, when discounted at the bank for 6 months, at 6 per cent., the borrower may receive $365? Ans. $376 483. 7. What must be the amount of a note, so that, when discounted at the bank for 9 months, at 7 per cent., the borrower may receive $500? Ans. $527.03. 73. The banks, by this method of discounting, obtain a larger per cent. for their money than 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 1 year, at 7 per cent., he receives $0.93; the $0.07 is retained by the bank, it being the interest of $1 for 1 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: 3 1+1õõ+(1õõ)2 +(ïõõ)3+, &c.; this, summed, disregarding the 3 days of grace, gives 10752688. 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 14 years, at 7 per cent. In this case, the interest would equal the whole face of the note; so that the bank would withhold the whole amount, be that ever 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 14 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 14 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 |