3. Of $325.25, due 18 months hence, at 6 per cent. ? 4. Of $250, payable in 3 years, at 6 per cent.? 5. Of $401.25, due 1 year hence, at 7 per cent. ? 6. Of $450, due 6 months hence, at 6 per cent.? 7. Of $63.60, due 1 year hence, at 6 per cent. ? 8. Of $384.80, due 3 years and 5 months hence? 9. A rote for $500, to be paid Dec. 20, 1846: what is the discount June 11, 1845?

10. A note for $1431, dated August 19, 1844, which becomes due January 13, 1845: what is the discount September 27, 1844?

11. A note becomes due Nov. 29, 1845, for $2744. 25: what is the discount Jan. 6, 1845?

12. Sold goods for $748.80, one half to be paid at 3 months, and the other half at 6 months: what must be the discount for the present payment, at 5 per cent.?

13. How much is the discount of $853, at 2 per cent.? 14. How much is the discount of $985.75, at 4 per cent.? 15. What is the discount on $2575, due in 4 months

hence?

Q. What is discount?

Q. What is the rule for finding the present worth of a given sum?

Q. How do you find the discount?

BANKING.

§ 138. A bank is an incorporated institution, created for the purpose of loaning money and dealing in exchange. Its capital is limited by law, and owned in shares by individuals called stockholders.

Banks are by law allowed to make notes, which are called bank bills, which circulate as money, because they are obliged to redeem them with specie.

When the banks loan money, it is customary to take the interest in advance; that is, to deduct it from the face or amount of the note, at the time the money is lent. The note is then said to be discounted.

The sum discounted is called the amount; the interest deJucted the discount; and what remains the proceeds or present worth.

A note to be discounted, or bankable, must be made payable at some future time, and to the order of some person who endorses it.

The drawer is not obliged to pay his note till three days after the expiration of the time mentioned in it, these being called days of grace.

1

of

Banks take interest for four days more than the number intervening between the day when a note is discounted, and the day on which the time specified in it expires, taking the rate per cent. per annum, for each 30 days of the time so estimated. Thus, on a note dated August 31, payable in 6 months, falling due February 28, days of grace expiring March 3, and which is discounted on the day of date, at the rate of 6 per cent. per annum, interest would be taken for 185 days 61 months 312 per cent.

=

§ 139. CASE 1. To find the banking discount, and present worth of any sum of money.

RULE. Calculate the interest on the given sum for four days more than the time specified, then deduct the interest from the amount; the remainder will be the present worth.

EXAMPLES.

1. What is the bank discount on $450, payable 180 days hence, at 6 per cent per annum?

days.

180

.06

4

13.50 Int. for 180

45

45

30 66

4

$13.80 discount.

66

days.

4 .03 Int. on $1 for 180
.0006
66
.03063

Therefore $450x.03063-$13.80 discount.

4

184

2. What is the bank discount on $600, payable 90 days hence, at 6 per cent.; and what is the present worth?

3. If I have a note of $9000, payable in 45 days, discounted at 6 per cent., what sum should I receive?

4. What is the bank discount on $750, payable 99 days hence, at 7 per cent.?

5. On $1800, payable 90 days hence, at 5 per cent.? 6. On $4200, payable 276 days hence, at 6 per cent.? 7. The present worth of a note for $3600 payable in 120 days, discounted at 6 per cent.?

8. Of a note for $1520, payable in 150 days, discounted per cent.?

at 6

9. Of a note for $5184, payable in 90 days, discounted at 6 per cent.?

10. Of a note for $3930, payable in 180 days, discounted at 6 per cent.?

11. What is the bank discount, at 6 per cent., on $675.68, payable in 30 days?

12. What sum should be paid at bank, for a note for $4000, payable in 60 days, discounted at 6 per cent.?

$140. CASE 2. To find what sum or amount must be named in a note, in order to obtain a particular loan at bank. RULE. Calculate the banking discount on $1, for the given rate and time; subtract this discount from $1, and divide the present worth by the remainder, and the quotient will be the amount.

EXAMPLES.

1. What must be the face or amount of a bankable note, so that when discounted for 210 days, at 6 per cent per annum, its present worth shall be $400?

2. What must be the face of a bankable note, so that when discounted for 60 days, at 6 per cent., it shall give a present worth of $7421.25?

3. Suppose your note is discounted at bank for 180 days, at 6 per cent., and $967.50 passed to your credit; what must have been the face of the note?

4. What must be the face of a bankable note, so that when discounted for 60 days, at 7 per cent., the borrower shall receive $150?

5. What must be the face of a bankable note, so that when discounted for 300 days, at 5 per cent., the present worth may be $6000 ?

6. What must be the face of a bankable note, so that when discounted for 150 days, at 6 per cent., it shall give a present worth of $1481.24?

EQUATION OF PAYMENTS.

141. Equation of payments is a rule for finding the average or equated time of several sums had at different dates or on different terms of credit, or both; in order that the whole amount due may be paid in

one sum.

Note. In sums to be equated no account is taken of a fraction of a dollar, if less than a half: if as great as a half, it is counted as a dollar. The same rule is applied to a fraction of a day in the equated time.

CASE 1. When the sums due have been obtained at the same date, but have different terms of credit.

RULE. Multiply each sum by its time of credit; add the products together, and divide their sum by the sum of the payments: the quotient will be the average time of credit.

EXAMPLES.

1. A owes B $560, of which $200 is to be paid at 3 months, $200 at 5 months, $100 at 6 months, and the rest at 9 months: required the equated time for the whole payment.

2. A merchant has owing to him $300, to be paid as follows: $50 at 2 months, $100 at 5 months, and the rest at 8 months; but it is agreed to make one payment of the whole: when should that be?

3. A debt of $3600 is to be paid as follows: at 3 months, at 4 months, at 5 months, at 6 months, and the rest at 7 months: what is the equated time for the whole ?

CASE 2. When the sums due have been obtained at different dates, but on similar terms of credit.

RULE. Multiply each sum by the number of days from its date to that of the last sum. Divide the sum of the products by the whole debt. The quotient will be the number of days prior to the date of the last sum, at which the average or equated date of purchase should be fixed.

EXAMPLES.

A purchased of B, on 6 months credit, as follows: May 4, $200, June 6, $600, August 20, $300. What is the equated time of purchase? $200 X 108=21600

C purchased of D, on 8 months credit, as follows: March 12, $500, May 3, $900, July 6, $300. What is the equated time of purchase? Ans. April 29.

E purchased of F, on 9 months credit, as follows: March 20, $1200, May 18, $560, August 27, $1680, September 23, $750. Required the equated time of purchase. Ans. July 4.

CASE 3. When the sums due have been obtained at different times. and on different terms of credit.

RULE. Multiply each sum by the number of days from the date when due to the latest date of payment. Divide the sum of the several products by the whole debt. The quotient will be the number of days prior to the latest date of payment, at which the average or equated date should be fixed.

EXAMPLES.

N purchased of O the following amounts, at the dates and credits respectively named. March 2, $400, at 8 months; April 25, $200, at 4 months; May 10, $900, at 6 months; June 7, $300, for cash. When will the whole amount be due?

36 days prior to Nov. 10- Oct. 5. Ans. (Payment to be made Oct. 8; 3 days grace being allowed on payments, in the United States.)

R bought goods of S; the amounts, dates and credits of his several purchases being as follows: March 1, $840, at 8 months; April 9, $1206, at 6 months; August 26, $1525, for cash; and October 3, $767, at 7 months. Required the date when the whole amount will be due? Ans. November 3.

Towes V for bills of goods of the following amounts, purchased at the dates and on the credits respectively named: April 3, $1256, at 8 months; April 30, $625.75, at 7 months; May 21, $520.37, for cash; August 25, $816, at 6 months; September 19, $1286.62, at 8 months; and October 12, $906.50, at 6 months. When will the whole amount be due ? Ans. January 27.

Equated time is also frequently ascertained thus: Find the interest on each item of indebtedness for the number of days, (or months and fractions of months) by which it would be multiplied in calculating by the preceding rules. Add together their several items of interest, and find in how many days the interest calculated on the whole amount of indebtedness would produce a similar sum. The number of days, thus ascertained, will be the equated time of credit in Case 1; and in Cases 2 and 3 will be the number of days prior to the date of purchase and of payment respectively, at which the equated date should be fixed.

BARTER.

§ 142. Barter is the exchange of one commodity for another, without loss to either party.

§ 143. CASE 1. When the quantity of one commodity is given with its value, to find what quantity of the other, at the rate proposed, may be had for the same money.

RULE. Find the value of that commodity whose quantity is given; then divide the value of the quantity exchanged by the price of an unit returned.