10. What is the amount of $.10 for 20 years, at 7 per cent. ? Ans. $.38696.

DISCOUNT.

325. Discount is an abatement or allowance made for the payment of a debt before it is due.

326. The Present Worth of a debt, payable at a future time without interest, is such a sum as, being put at legal interest, will amount to the given debt when it becomes due.

1. A owes B $321, payable in 1 year; what is the present worth of the debt, the use of money being worth 7 per cent.?

OPERATION.

ANALYSIS. The Am't of $1, 1.07) $321 ($300, Present value. amount of $1 for

321

$321 Given sum or debt.

300 Present worth.

$21 Discount.

1 year is $1.07; therefore the present worth of every $1.07 of the given debt is $1; and the present worth

of $321 will be as many dollars as $1.07 is contained times in $321. $3211.07=$300, Ans. Hence the following

RULE. I. Divide the given sum or debt by the amount of $1 for the given rate and time, and the quotient will be the present worth of the debt.

II. Subtract the present worth from the given sum or debt, and the remainder will be the discount.

NOTE. The terms present worth, discount, and debt, are equivalent to principal, interest, and amount. Hence, when the time, rate per cent., and amount are given, the principal may be found by (321); and the interest by subtracting the principal from the amount.

EXAMPLES FOR PRACTICE.

2. What is the present worth of $180, payable in 3 years 4 months, discounting at 6 %?

Ans. $150.

Define discount. Present worth. Give analysis. Rule.

3. What is the present worth of a note for $1315.389, due in 2 years 6 months, at 7 per cent.? Ans. $1119.48.

4. What is the present worth of a note for $866.038, due in 3 years 6 months and 6 days, when money is worth 8 per cent.? What the discount? Ans. $190.15+, discount.

5. What is the present worth of a debt for $1005, on which $475 is to be paid in 10 months, and the remainder in 1 year 3 months, the rate of interest being 6 %?

NOTE. When payments are to be made at different times without interest, find the present worth of each payment separately, and take their sum. Ans. $945.40+.

6. I hold a note against C for $529.925, due Sept. 1, 1859; what must I discount for the payment of it to-day, Feb. 7, 1859, money being worth 6 %? Ans. $17.425.

7. A man was offered $3675 in cash for his house, or $4235 in 3 years, without interest; he accepted the latter offer; how much did he lose, money being worth 7 per cent.? Ans. $175. 8. A man, having a span of horses for sale, offered them for $480 cash in hand, or a note of $550 due in 1 year 8 months, without interest; the buyer accepted the latter offer; did the seller gain or lose thereby, and how much, interest being 6 %? Ans. Seller gained $20.

9. What must be discounted for the present payment of a debt of $2637.72, of which $517.50 is to be paid in 6 months, $793.75 in 10 months, and the remainder in 1 year 6 months, the use of money being worth 7 per cent.? Ans. $187.29 + 10. What is the difference between the interest and discount of $130, due 10 months hence, at 10 %? Ans. $.83.

PROMISCUOUS EXAMPLES IN PERCENTAGE.

1. A merchant bought sugar in New York at 61 cents per pound; the wastage by transportation and retailing was 5 per cent., and the interest on the first cost to the time of sale was 2 per cent.; how much must he ask per pound to gain 25 per cent.? Ans. 81+ cents.

2. A person purchased 2 lots of land for $200 each, and sold one at 40 per cent. more than cost, and the other at 20 per cent. less; how much did he gain? Ans. $40.

3. Sold goods to the amount of $425, on 6 months' credit, which was $25 more than the goods cost; what was the true profit, money being worth 6 %? Ans. $12.62+.

4. Bought cotton cloth at 13 cents a yard, on 8 months' credit, and sold it the same day at 12 cents cash; how much did I gain or lose per cent., money being worth 6 per cent.? Ans. Lost 4 %.

5. A farmer sold a pair of horses for $150 each; on one he gained 25 per cent., on the other he lost 25 per cent.; did he gain or lose on both, and how much? Ans. Lost $20.

6. A man invested of all he was worth in the coal trade, and at the end of 2 years 8 months sold out his entire interest for $3100, which was a yearly gain of 9 per cent. on the money invested; how much was he worth when he commenced trade? Ans. $3750.

7. In how many years will a man, paying interest at 7 per cent. on a debt for land, pay the face of the debt in interest? Ans. 14 years.

8. Two persons engaged in trade; A furnished & of the capital, and B ; and at the end of 3 years 4 months they found they had made a clear profit of $5000, which was 124 per cent. per annum on the money invested; how much capital did each furnish? Ans. A, $7500; B, $4500.

9. Bought $500 worth of dry goods, and $800 worth of groceries; on the dry goods I lost 20 per cent., but on the groceries I gained 15 per cent.; did I gain or lose on the whole investment, and how much? Ans. Gained $20. 10. What amount of accounts must an attorney collect, in order to pay over $1100, and retain 8 per cent. for collecting? Ans. $1200.

11. A merchant sold goods to the amount of $667, to be paid in 8 months; the same goods cost him $600 one year previous to the sale of them; money being worth 6 per cent., what was his true gain? Ans. $5.346+.

12. A nurseryman sold trees at $18 per hundred, and cleared of his receipts; what per cent. profit did he make? Ans. 50 %.

13. If of an article be sold for what ğ of it cost, what is the gain per cent.? Ans. 40g.

14. A lumber merchant sells a lot of lumber, which he has had on hand 6 months, on 10 months' credit, at an advance of 30 per cent. on the first cost; if he is paying 5 per cent. interest on capital, what are his profits per cent.? Ans. 217.

15. A person, owning § of a piece of property, sold 20 per cent. of his share; what part did he then own?

Ans.

16. A speculator, having money in the bank, drew 60 per cent. of it, and expended 30 per cent. of 50 per cent. of this for 728 bushels of wheat, at $1.121 per bushel; how much was left in the bank? Ans. $3640.

17. I wish to line the carpet of a room, that is 6 yards long and 5 yards wide, with duck yard wide; how many yards of lining must I purchase, if it will shrink 4 per cent. in length, and 5 per cent. in width? Ans. 43. 18. A's money is 28 per cent. more than B's; how many per cent. is B's less than A's? Ans. 213.

19. A capitalist invested of his money in railroad stock, which depreciated 5 per cent. in value; the remaining he invested in bank stock, which, at the end of 1 year, had gained $1200, which was 12 per cent. of the investment; what was the whole amount of his capital, and what was his entire loss or gain? Ans. $25000, capital; $450, gain. 20. C's money is to D's as 2 to 3; if of C's money be put at interest for 3 years 9 months, at 10 per cent., it will amount to $1933.25; how much money has each?

Ans. C, $2812; D, $4218

BANKING.

327. A Bank is a corporation chartered by law for the purpose. of receiving and loaning money, and furnishing a paper circulation.

What is a bank?

328. A Promissory Note is a written or printed engagement to pay a certain sum, either on demand or at a specified time.

329. Bank Notes, or Bank Bills, are the notes made and issued by banks to circulate as money. They are payable in specie at the banks.

330 The Face of a note is the sum made payable by the note.

331. Days of Grace are the three days usually allowed by law for the payment of a note after the expiration of the time specified in the note.

332. The Maturity of a note is the expiration of the days of grace; a note is due at maturity.

333. Notes may contain a promise of interest, which will be reckoned from the date of the note, unless some other time be specified.

The transaction of borrowing money at banks is conducted in accordance with the following custom: the borrower presents a note, either made or indorsed by himself, payable at a specified time, and receives for it a sum equal to the face, less the interest for the time the note has to run. The amount thus withheld by the bank is in consideration of advancing money on the note prior to its maturity.

334. Bank Discount is an allowance made to a bank for the payment of a note before it becomes due.

335. The Proceeds of a note is the sum received for it when discounted, and is equal to the face of the note less the discount.

CASE I.

336. Given the face of a note to find the proceeds. The law of custom at banks makes the discount of a note

Bank notes.

Define a promissory note. The face of a note. Days of grace. The maturity of a note. Explain the process of discounting a note at a bank. Define bank discount. The proceeds of a note. What is Case I?