2. What is the amount of $100, at 6 per cent. per annum, compound interest, for two years, when the interest is added in at the end of every six months?

3. What is the compound interest of $630, for 4 years, at 5 per cent.?

Ans. $135 769. 4. What is the amount at compound interest, of $50, for 3 years, at 5 per cent. ?

Ans. $57.881. 5. What is the compound interest of $1000, for 4 years, at 6 per cent. ?

Ans. $262.477.

BANKING.

119. 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 caller stockholders.

Banks are allowed to make notes which are denomi

nated bank bills, which circulate as money, because, on demand of the holders of them, they must be redeemed by the banks, 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 then 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 the interest for 3 days more than the time specified in the note; and the borrower is not obliged to make payment till these three days have ́expired, which are for this reason called days of grace.

What is a bank? What is the stock? Who are the stockholders? How are bank notes called? Do they circulate as money? How are the banks obliged to redeem their notes? How do banks sometimes take the interest? When is a note said to be discounted? What is the amount? What is the interest deducted called? How is that which remains called? Does a bank note require an indorser? For how many days more than specified in the note do banks take interest? What are these three days called?

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

*This method of discounting bank notes is usurious, and is fast going out of use, and instead of it the banks now deduct the discount as found by Rule under ART 112.

per cent.; this, increased by its sixth part, becomes $18.084 for the discount at 7 per cent., as required. Hence we may find banking discount by the following

RULE.

Compute the interest (Case IV. ART. 113,) on the given sum, for three days more than is specified. This interest will be the discount.

EXAMPLES.

1. What is the banking discount of $150, for 6 months, at 6 per cent.? Ans. $4.575. 2. What is the banking discount of $375, for 3 months and 9 days, at 7 per cent.? Ans. $7.438. 3. What is the banking discount of $400, for 9 months, at 7 per cent.? Ans. $21.231. 4. What is the banking discount of $29-30, for 7 months, at 5 per cent.?

Ans. $0.867. 5. What is the banking discount of $472, for 10 months, at 7 per cent.? Ans. $27.809.

120. When the present worth of a bankable note, the time for which it is to be discounted, and the rate per cent. are given, to find the amount or face of the note.

What must be the face of a bank note which, when discounted for 4 months and 15 days, gives a present worth of $100, interest being 6 per cent.?

If we suppose the note to be $1, we find the banking discount for 4 months and 15 days to be $0.023; hence $1-$0.023=$0.977, is the present worth. Had the face of the note been $2, the present worth would have been twice $0.977; had it been $10, ten times $0.977, and the same would be true for other ratios. Hence, in order

that the present worth of the note may be $100, its face must be as many times greater than $1, as $100 is times greater than $0-977. Dividing $100 by $0-977, we find for a quotient 102-354+. Hence, if a bank note for $102.35 be discounted for 4 months and 15 days at 6 per cent. interest, the present worth will be $100. Hence 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 amount, or face of the note.

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; therefore, 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.

22

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 7 per cent., the present worth may be $70.50? Ans. $73.546.

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.