26. If money be worth 7%, compounded annually, which would be better, and how much, for a capitalist to loan $25000 for 11 years and 6 months, than to invest it in land that, at the end of the time named, will sell for $55000 above all expenses for taxes?

27. I loaned a bridge builder $17500 for 7 years, at 10% per annum, interest payable quarterly, and took a bond and mortgage to secure the debt and its interest. Nothing having been paid until the end of the 7 years, how much was required in full settlement?

28. On the 20th of March, 1888, I borrowed $13500, at 5% interest; on April 5 I loaned $5000 of the money until Dec. 20, 1888, at 8%; April 15, I purchased with the remainder a claim for $10000, due Aug. 1, but which, not being paid at maturity, was extended until the $5000 became due, at the rate of 6%. How much did I gain, both claims having been paid on the day the loan of $5000 became due?

29. Having bought a mill for $12000, I paid cash $4000 on delivery, and gave a bond and mortgage for 8 years without interest to secure the balance; to secure the interest, which was to be paid semi-annually, at the rate of 7% per annum, I gave sixteen non-interest bearing notes, without grace, for $280 cach, one maturing at the end of each 6 months for the 8 years. If the four of the notes first maturing were paid when due, and no other payment was made until the mortgage became due, how much was required for full settlement?

30. Charles will be 11 years old Dec. 15, 1888, John will be 8 years old July 28, and Walter was 5 years of age April 30. If, on July 1, a 6% compound interest investment be made for each, so that at the age of 21 he may have $10000, what amount of cash will be required, the interest being compounded quarterly?

TRUE DISCOUNT.

740. Discount is an abatement or allowance made from the amount of a debt, a note, or other obligation, or a deduction from the price of goods for payment before it is due.

741. The Present Worth of a debt payable at a future time without interest, is its value now; hence, is such a sum as, being put at simple interest at the legal rate, will amount to the given debt when it becomes due.

742. True Discount is the difference between the face of a debt due at a future time and its present worth.

REMARKS.-1. To find present worth, apply the principles given in INTEREST. The debt corresponding to the amount; the rate per cent. agreed upon to the rate; the time intervening before the maturity of the debt, to the time; and the present worth, which is the unknown term, is the principal.

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

3. With debts bearing interest, and discounted at the same or at a different rate of interest, the face of the debt plus its interest as due at maturity becomes the base.

743. To find the Present Worth of a Debt.

EXAMPLE. Find the present worth and true discount of a claim for $871.68, due 2 yr. 3 mo. hence, if money is worth 6% per annum.

EXPLANATION.-The amount of the debt at the end of 2 yr. 3 mo. is $871.68; and since $1 would in that time, at 6 per cent., amount to $1.135, the present worth must be as many times $1 as $1.135 is contained times in $871.68, or $768. If the face of the debt is $871.68, and its present worth is only $768, the true discount will be $871.68 minus $768, or $103.68.

Rule.-Divide the amount of the debt, at its maturity, by one dollar plus its interest for the given time and rate, and the quotient will be the present worth; subtract the present worth from the amount, and the remainder will be the true discount.

EXAMPLES FOR PRACTICE.

744. 1. What is the present worth of $661.50, payable in 3 yr. 9 mo., discounting at 6%?

2. Find the present worth and true discount of a debt of $138.50, due in 5 yr. 6 mo. 18 da., if money is worth 7% per annum.

3. Find the present worth of a debt of $1750, $1000 of which is due in 9 mo. and the remainder in 15 mo., money being worth 6% per annum.

4. Which is greater, and how much, the interest, or the true discount on $516, due in 1 yr. 8 mo., if money is worth 10% per annum?

5. Which is better, and how much, to buy flour at $6.75 per barrel on 6 months time, or to pay $6 cash, money being worth 6%?

6. When money is worth 5% per annum, which is preferable, to sell a house for $20,000 cash, or $21,000 due in one year?

7. A farmer offered to sell a pair of horses for $420 cash, or for $475 due in 15 months without interest. If money is worth 8% per annum, how much would the buyer gain or lose by accepting the latter offer?

8. If money is worth 6%, what cash offer will be equivalent to an offer of $1546 for a bill of goods on 90 days credit?

9. An agent paid $840 cash for a traction engine, and after holding it in stock for one year, sold it for $933.80, on eight months' credit. If money is worth 6%, what was his actual gain?

10. A stock of moquette carpeting, bought at $1.95 per yard, on 8 months' credit, was sold on the date of purchase for $1.80 per yard, cash. If money was worth 6% per annum, what per cent. of gain or loss did the seller realize?

11.

Marian is now fifteen months old. How much money must be invested for her, at 6% simple interest, that she may have $15000 of principal and interest when she celebrates her eighteenth birthday?

12. A thresher is offered a new machine for $480 cash, $500 on 2 months credit, or $525 on 1 year's credit. Which offer is the most advantageous for him, and how much better is it than the next best, with money worth 7%?

13. After carrying a stock of silk for 4 months, I sold it at an advance of 30% on first cost, extending to the purchaser a credit of one year without interest. If money is worth 5% per annum, what was my per cent. of profit or loss?

14. Having bought a house for $5048 cash, I at once sold it for $7000, to be paid in 18 months without interest. If money is worth 8% per annum, did I gain or lose, and how much?

15. Goods to the amount of $510 were sold on 6 months' credit. If the selling price was $30 less than the goods cost, and money is worth 6% per annum, how much was the loss and the per cent. of loss?

16. How much must be discounted for the present payment of a debt of $8741.50, $2000 of which is on credit for 5 months; $3000 for 8 months, and the remainder for 15 months, money being worth 10% per annum?

17. What amount of goods, bought on 6 months time or 5% off for cash, must be purchased, in order that they may be sold for $4180, and net the purchaser 10% profit, he paying cash and getting the agreed discount off?

18. A dealer bought grain to the amount of $2700, on 4 months' credit, and immediately sold it at an advance of 10%. If from the proceeds of the sale he paid the present worth of his debt at a rate of discount of 8% per annum, how much did he gain?

19. A merchant bought a bill of goods for $2150, on 6 months' credit, and the seller offered to discount the bill 5% for cash. If money is worth 71% per annum, how much would the merchant gain by accepting the seller's offer.

20. The asking price of a hardware stock is $5460, on which a trade discount of 25%, 15%, and 10% is offered, and a credit of 90 days on the selling price. If money is worth 51%, what should be discounted for the payment of the bill ten days after its purchase?

21. A merchant sold a bill of goods for $1800, payable without interest in three equal payments, in 3 months, 6 months, and 9 months respectively. If money is worth 5% per annum, how much cash would be required for full settlement on the date of purchase?

22. A stationer bought a stock worth $768, at a discount of 25% on the amount of his bill, and 4% on the remainder for cash payment. He at once sold the stock on 4 months' time, at 10% in advance of the price at which it was billed to him. How much will the stationer gain if his purchaser discount his bill on the date of purchase by true present worth, at the rate of 7% per annum?

23. I sold my farm for $10,000, the terms being one-fifth cash, and the remainder in four equal semi-annual payments, with simple interest at 5% on each from date; three months later the purchaser settled in full by paying with cash the present worth of the deferred payments, on a basis of 10% per annum for the use of the money. How much cash did I receive in all ?

24. What amount of goods, bought on 4 months' time, 10% off if paid in 1 month, 5% off if paid in 2 months, must be purchased, in order that they may be sold for $11480, and the stock net a profit of 15% and the remainder a profit of 20% to the purchaser, if he cashes his purchase within 1 month and gets the agreed discount off?

BANK DISCOUNT.

745. A Bank is a corporation chartered by law for the receiving and loaning of money, for facilitating its transmission from one place to another by means of checks, drafts, or bills of exchange, and, in case of banks of issue, for furnishing a paper circulation.

REMARK.-Some banks perform only a part of the functions above mentioned.

746. Negotiable Paper commonly includes all orders and promises for the payment of money, the property interest in which may be negotiated or transferred by indorsement and delivery, or by either of those acts.

747. Bank Discount is a deduction from the sum due upon a negotiable paper at its maturity, for the cashing or buying of such paper before it becomes due.

748. The Proceeds of a Note or other negotiable paper is the part paid to the one discounting it, and is equal to the face of the note, less the discount. REMARK.-In true discount, the present worth is taken as the principal; in bank discount the future worth is taken as the principal.

749. The Face of a Note is the sum for which it is given.

750. The Discount may be a fixed sum, but is usually the interest at the legal rate, and taken in advance.

751. The Time in bank discount is always the number of days from the date of discounting to the date of maturity.

752. The Term of Discount is the time the note has to run after being discounted.

REMARK.-Bank discount is usually reckoned on a basis of 360 days for a year.

753. A Promissory Note is a written, or partly written and partly printed, agreement to pay a certain sum of money, either on demand or at a specified time. REMARK.—In general, notes discounted at banks do not bear interest. If the note he interestbearing, the discount will be reckoned on and deduced from the amount due at maturity. 754. 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.

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

REMARKS.-1. Notes containing an interest clause will bear interest from date to maturity, unless other time be specified.

2. Non-interest bearing notes become interest bearing if not paid at maturity.

3. The maturity of a note or draft is indicated by using a short vertical line, with the date on which the note or draft is nominally due on the left, and the date of maturity on the right; thus. Oct. 21/24.