interest, would amount to the debt at the time when the debt becomes due.

Hence,

The DISCOUNT is the difference between the debt and the present worth.

ART. 258. In all computations of discount it is necessary first to find the present worth.

Ex. 1. What is the discount on a debt of $457.92, payable in 9 months, when money is worth 8 per cent.?

Analysis. The amount of $1 in 9 months at 8% is $1.06; therefore $1.06 due in 9 mouths is worth $1 now. Hence, if the sum of 106 cents due 9 months hence is worth $1 now, then 1 cent due 9 months hence is worth of $1 now = $1865 and $457.92, or 45792 cents, will be worth 45792 times as much now $45792 $432, which is the present worth. Subtracting $432, the present worth, from the debt, we have $25.92 as the discount. Ans. $25.92. The foregoing Analysis illustrates the reason for the following

RULE.

I. Divide the given debt by the amount of one dollar for the given time, at the given rate; the quotient will be the PRESENT

WORTH.

II. Subtract the PRESENT WORTH from the DEBT, and the remainder will be the DISCOUNT.

EXAMPLES.

2. What is the discount of $897.82, payable in 3 years, when money is worth 7 per cent.? Ans. $155.82.

3. What is the present worth of $787.75, due in 2yr. 6mo., when money is worth 6%?

Ans. $685.

4. What is the discount on a note for $1174.32, due in 3yr. 3mo, money being worth 8% ? 5. A note for $1380.06 becomes due in 15 months; what

Ans. $242.32.

deduction should be made for the immediate payment of the money, supposing money to be worth 8% ? Ans. $125.46.

6. A merchant of Macon buys in Boston a bill of dry goods amounting to $2513.79 on a credit of 4 months; a bill of crockery for $469.68, payable in 6 months; and a bill of groceries for $1691.75, due in 2 months; how much ready cash will pay all the bills, discounting at 6 per cent.?

Ans. $4595.50.

7. Which is worth most-$750 cash down, $765 payable in 3 months, or $780 payable in 6 months, money being worth 8%?

Ans.

BANK DISCOUNT.

ART. 259. A bank is an institution one of whose chief objects is to lend money. When money is borrowed from a bank, the interest is always paid in advance, or at the time of receiving the money. Thus, if a man gives his note for $500, payable in 3 months, at 7 per cent., he will receive from the bank only $491.25; as $8.75 would be retained to pay the interest on the $500 for the 3 months. This $8.75 is called BANK DISCOUNT. Hence,

ART. 260. BANK DISCOUNT is really simple interest paid in advance.

ART. 261. A note is said to be discounted at a bank when the note is received by the bank, and the holder of the note receives the money for it after the bank discount is deducted. That which is left after deducting the discount from the face of the note is called the NET PROCEEDS.

ART. 262. It is the custom with banks to allow three days more time in which to pay a note than is specified on the face of the note. These three days are called "DAYS OF GRACE.” In calculating the discount the three "days of grace" are always taken into the account. As bank discount is nothing

more than simple interest, we have for its computation the following

RULE.

I. Calculate the interest on the face of the note for the specified time, together with the three “days of grace;" this will give the

BANK DISCOUNT.

II. Subtract the bank discount from the face of the note; the remainder will be the NET PROCEEDS.

EXAMPLES.

1. What is the bank discount on a note for $1250 payable in 3mo., with interest at 6% ?

Ans. $19.375. 2. A note for $2016, payable in 4 months, was discounted at a bank at 8%; what was the bank discount?

Ans. $55.104. 3. What are the proceeds of a note for $1650, due in 2 months, discounted at a bank at 6%? Ans. $1632.675.

4. A merchant in New York sells a grocer of Atlanta a bill of sugar amounting to $2260, for which he receives a note payable in 3mo., with interest at 6%. If the merchant discounts his note at the "First National Bank of New York," what sum will he receive from the bank? Ans. $2224.97.

ART. 263. In the practical operations of business it is often necessary to know for what particular amount to draw a bank able note, payable at some definite period, so that when dis counted at a bank it may yield a specified sum. The prin ciples of Bank Discount enable us to solve this problem.

Ex. 1. For what sum must I draw a note, payable in 3mo. 15da., so that, when discounted at a bank at 6%, the proceeds may be $725?

Analysis. According to the preceding article, the bank dis count on $1, at 6%, for 3mo. 15da., together with the three "days of grace," is $0 018. Subtracting this bank discount

from $1, we obtain $0.982 as the proceeds of a note for $1. We sce, therefore, that for each $0.982 of proceeds the note must contain $1; hence, the note must contain as many dollars as $0.982 is contained times in the proceeds. Therefore, dividing $725 by $0.982, we have $738.289 as the face of the note. Ans. $738.289.

From the foregoing explanation we deduce a

RULE.

Divide the given sum by the PROCEEDS of $1 for the given rate and time; the quotient will be the FACE of the note

EXAMPLES.

2. For what sum must a note be drawn so that, discounted at a bank for 3mo. 15da., at 8%, the proceeds may be $864? Ans. $885.245 +.

3. A grocer in Eufaula, Ala., owes a merchant in Augusta, Ga., $1275; how large must the grocer draw his note, payable in 8mo. 9da., that, discounted at the Georgia Railroad Bank at 9%, the money received will just pay the Augusta merchant? Ans. $1360.725 +.

4. What must be the face of a note, payable in 5mo. 3da., so that, discounted at a bank at 6%, the maker may receive $1240? Ans. $1273.10 +.

ART. 264. A very simple and convenient method of finding the face of a bankable note has been devised by J. II. Sawyer, Esq., Assistant Cashier of Citizens' Savings Bank, Columbia, S. C, which is as follows:

If we divide 360 (bankers' year) by 1 per cent., or .01, we get the quotient 36000; dividing by 2%, we have 18000; by 3%, 12000; 4%, 9000; and so on. Calling these several quotients REPRESENTATIVES of their corresponding per cents., we have the following

To show the application, let us take an example:

Ex. 1. What must be the face of a note which, discounted at 8% for 3 months, will give $675 as the net proceeds?

Ans. $689.244.

Reference to the above Table shows 4500 to be the representative of 8 per cent. From 4500 we subtract 93 (the number of days the note is to run, and three "days of grace" added); the remainder, 4407, we take for a divisor. We now multiply $675 (the net proceeds) by 4500; the product is 3037500, which we call a dividend. Dividing 3037500 by 4407, we have as the quotient $689.244; and this is the face of the note.

The process employed may be summed up in the following

RULE.

I. Subtract the number of days the note has to run, including the three days of grace, from the REPRESENTATIVE of the “ate of interest for a DIVISOR.

II. Multiply the given sum by the representative of the rate of interest for a DIVIDEND. Divide the dividend by the divisor, and the quotient will be the FACE of the note.

EXAMPLES.

2. Required the face of a note payable in 5mo. 15da., sc that, discounted at 6%, the holder may receive $450.

Ans. $462.962.