16. What is the difference between the simple Int. and discount of $1080 for 10 yr., at 6%? Ans. $243.

17. A man was offered $1122 for a house, in cash, or $1221, payable in 10 mon. without Int. He chose the latter how much did he lose, supposing the note discounted at the rate of 12 % per annum? Ans. $12.

ART. 237. PAYMENTS AT DIFFERENT TIMES.

When payments without interest, are to be made at different times, to find the present value of the whole,

Find the present worth of each payment, and take their sum. 18. Find the present value of a debt of $956.34, onethird to be paid in 1 yr., one-third in 2 yr., and one-third in 3yr.; money being worth 5 %. Ans. $870.60

19. Of a debt of $1440, of which one-half is payable in 3 mon., one-third in 6 mon., and the remainder in 9 mon.; Int. at 6 % per annum. Ans. $1405.044+

20. Of a debt of $700, of which $60 are to be paid in 6 mon., $180 in 1yr., $260 in 18 mon., the remainder in 2 yr.; Int. 6% per annum. Ans. $645.167+

DISCOUNT AND INTEREST COMPARED.

ART. 238. A comparison of Discount with Interest (Art. 219), shows that the Present Worth corresponds to the principal, the debt to the amount, and the discount to the interest of the principal for the given time, at the given rate per cent.; hence,

When the time, rate per cent., and amount are given, the principal is found (Art. 236) by dividing the amount by the amount of $1 for the given time, at the given rate per cent. To find the interest, subtract the principal from the amount. 1. The amount is $650; time, 5yr.; rate, 6 %: what is the principal? Ans. $500.

REVIEW.-236. How find the present worth, Rule? The discount? How, by proportion? 237. When payments without interest are to be made at different times, how find the present value of the whole?

2. What principal, at interest for 9 yr., at 5%, will amount to $725?

Ans. $500.

3. The amount is $571.20; time, 4 yr.; rate, 5 %: what is the interest? Ans. $95.20 4. A note, at interest for 2 yr. 6 mon., at 6 %, amounts to $690: find the interest.

ART. 289. BANK DISCOUNT.

Ans. $90.

A PROMISSORY NOTE is a written promise by one or more persons to pay to another, a named sum of money, after a specified time has elapsed from its date.

A note is discounted when a bank receives it, and pays to the holder what remains after deducting from its fuce the interest on it, till it becomes due.

BANK DISCOUNT is the interest deducted from the face of the note.

The bank discount, therefore, is the Simple Interest of the FACE of the note paid in advance.

The time to elapse from any given date till a note becomes due, is termed days to run. By usage, a note or draft is not really due till three days after the time specified for payment.

These three days are called DAYS OF GRACE, but banks charge interest for them.

Hence, in calculating the interest, three days must be added to the time specified in the note.

The FACE of a note is the sum promised to be paid; the PROCEEDS, the sum realized when the note is discounted.

REM.-1. Before a bank discounts a note, it is required that one or more persons shall indorse it; that is, write their names upon the back, by which they become responsible for its payment.

REVIEW.-238. Comparing discount with interest, to what does the present worth correspond? The debt? Discount? When the time, rate per cent., and amount are given, how find the principal? The interest? 239. What is a promissory note? What is bank discount? What are days to run? When is a note really due? What are days of grace? What is the face of a note? What the proceeds?

2. Bank discount is different from true discount. Art. 235. The bank discount of $106 for 1 year, is $6.36, while the true discount, Art. 236, is $6. The difference, 36 cents, is the interest of the true discount for the same time.

For a fuller discussion of this subject, see "Ray's Higher Arithmetic."

ART. 240. In bank discount, as interest is always to be computed for three days more than the specified time of payment, the calculations involve the finding of Int. for days; see Rule 2, Art. 225.

The rate per cent. is always 6, unless some other is given.

1. What is the bank discount and proceeds of a note of $100, payable 60 days after date?

Find the Bank discount of a note of 2. $137, payable 90 days after date. 3. $1780, payable 90 days after date. 4. $375, payable 30 days after date. 5. $165, payable 60 days after date. 6. $140, payable 4 mon. after date. 7. $80, payable 6 mon. after date.

Find the Proceeds or Avails of a note of

ANSWERS.

$2.12+ $27.59

$2.061

$1.731 $2.87 $2.44

REVIEW.-239. REM. 1. What is meant by indorsing a note? 2. Are bank discount and true discount the same? Show their difference by an example. 240. By what rule is bank discount generally calculated?

12. Find the proceeds of a note of $2580, due 100 days after date, discount 5%. Ans. $2543.09+

13. I bought 225 barrels flour, at $3.50 per bl. ; sold it at $4 per bl., taking a note payable 6 mon. after date. If this note be discounted at 6% per annum, what the gain by the transaction? Ans. $85.05

14. What the difference between true bank discount, of $535, for 1 year, at 7 %, days of grace?

discount, and not reckoning Ans. $2.45

15. Omitting the 3 days of grace, find the difference between the true and bank discount of $1209, for 4 yr., at 6% per annum. Ans. $56.16

ART. 241. To make a note, which, when discounted, the proceeds shall be a given sum.

1. For what sum, due 90 days hence, must I give a note, that when discounted at 6% per annum, the proceeds will be $177.21 ?

SOL. The bank discount of $1 for 93 da., is $.0155 (Art. 223); which, deducted, from $1, leaves $.9845, the proceeds of a note of $1, discounted for the same time. Therefore, for each $.9845 of proceeds, the note must contain $1; hence, the note must contain as many dol's as $.9845 is contained times in the proceeds.

$177.21$.9845=180.

Ans. $180.

PROOF-Interest of $180 for 93 da.=$2.79;

and $180 $2.79 $177.21

Hence, divide the proceeds of the note by the proceeds of $1 on the same conditions; the quotient will be the face of the note.

2. For what sum must a note be made, at 3 mon., so that, when discounted at a bank at 6%, the amount received will be $393.80 ? Ans. $400.

3. I wish to obtain $500 for 60 days: for what sum must the note be given? Ans. $505.305+

REVIEW.-241. How find the face of a note, which, when discounted, the proceeds shall be a given sum?

ART. 242. PROFIT AND LOSS

Are terms used to express the gain or loss in business. In Profit and Loss, four quantities are considered:

1st, the cost price; 2d, the selling price; 3d, the amount of gain or loss; 4th, the rate per cent. of gain or loss.

ART. 243. CASE I.

To find the AMOUNT of profit or loss, when the cost price and rate per cent. of gain or loss are given.

1. A merchant bought a piece of cloth for $40, and sold it at 10% profit: how much did he gain?

SOLUTION.-10 pr. ct. of $40 is $4, the required gain.

2. A merchant bought a bale of cotton for $80, which he sold at 8% loss: what did he lose?

SOLUTION.-8 pr. ct. of $80 is $6.40, the loss.

Rule for Case I.—Find the given per cent. of the cost price, and the result will be the gain or loss. Art. 210.

NOTE. The rate per cent. of gain or loss always refers to the purchase or cost price, and not to the selling price.

3. A merchant sold goods, that cost $150, and gained 10% what was his gain? Ans. $15.

4. A peddler sold goods, that cost $874, at a gain of 25% required his gain. Ans. $218.50

5. I bought goods for $500, and sold them at 12 % profit: what sum did they bring?

Ans. $560.

6. Sold goods that cost $382.50, at a loss of 4%: what sum did they bring? Ans. $367.20

ART. 244. CASE II.

To find the SELLING PRICE, when the cost price is known, so that a given rate % may be gained or lost.

REVIEW.-242. What are profit and loss? What four quantities are considered? 243. What is Case 1? What the Rule? NOTE. To what does the rate per cent. refer? 244. What is Case 2?