9. A certain sum of money on interest amounts at 4 per cent., for a certain time, to $1216, and at 10 per cent., for the same time, to $1600; required the principal and time. Ans. Prin. $960; Time, 6 yr. 8 mo.

CASE IV.

478. Given, the principal, the time, and the interest or the amount, to find the rute.

MENTAL EXERCISES.

1. At what rate will $60 in 5 years give $21 interest?

SOLUTION.-For 5 years at one per cent. 180 or

of the principal equals the interest; of $60 equals $3; if $60 in 5 years at one per cent. gains $3, to gain $21 it will require as many times 1 per cent. as $3 is contained times in $21, which are 7.

At what per cent. will

2. $40 in 5 yr. give $20 int. ? 3. $50 in 6 yr. give $15 int.? 4. $60 in 7 yr. give $21 int.? 8. At what rate will a principal times itself? 5 times itself?

5. $10 in 4 yr. give $12 am't? 6. $90 in 5 yr. give $117 am't? 7. $60 in 3yr. 4mo. give $70 am't? gain 2 times itself in 30 years? 4

9. At what rate will a principal double itself in 10 years? in 12 yr.? in 20 yr.? in 25 yr.?

10. At what rate will a principal treble itself in 20 years? in 25 yr.? in 40 yr.? in 80 yr.?

11. The amount of a certain principal for 7 years at a certain rate per cent. is $540, and for 10 yr. is $600; required the principal and the rate per cent.

WRITTEN EXERCISES.

1. At what rate will $234 give $49.14 interest in 3 yr. 6 mo. ?

SOLUTION. We find the interest of $234 for 3 yr. 6 mo., at one per cent., is $8.19. If the principal in the given time, at one per cent., gives $8.19 interest, to give $49.14 interest, it will require as many times one per cent. as $8.19 is contained times in $49.14, which is 6 per cent. Hence we have the following

OPERATION.
$234

.01

2.34

31

$8.19 int. at 1% 49.148.196%.

Rule.--Divide the given interest by the interest of the principal for the given time, at ONE per cent.

NOTE.-When the amount is given, subtract the principal from the amount to find the interest, and proceed as before.

2. At what rate will $240, in 5 yr. 4 mo., give $64 interest? Ans. 5%.

3. At what rate will $654, in 7 yr. 8 mo., give $350.98 interest? Ans. 7%.

4. At what rate will $72.50, in 3 yr. 4 mo. 15 da., give $14.6814 interest? Ans. 6%.

5. At what rate will $3975, in 6 yr. 7 mo. 20 da., give $2375.06 interest? Ans. 9%. 6. At what rate will $13.25, in 8 yr. 10 mo. 18 da., give $7.0624 interest? Ans. 6%. 7. The amount of a certain principal for 5 yr. at a certain rate is $2430, and for 12 yr., at the same rate, it is $3312; required the principal and the rate. Ans. $1800; 7%.

8. The amount of a certain principal for 4 yr., at a certain rate per cent., is $3551, and for 19 yr., $69293; required the principal and rate. Ans. Prin., $2650; Rate, 8%.

MENTAL EXERCISES.

1. A's fortune is $200, which is of B's; what interest will each receive on his money in 4 years, at 5% ?

2. C's money is $300, which is of D's money; what is the amount of the money of each on interest, for 5 years at 6 per cent.? 3. A's money is $400, which is of B's money; how much more interest will B receive than A in 8 years, at 5 per cent.?

4. The amount of $250 for 6 years at 10% is to be divided between C and D, so that C shall have 3 times as much as D; what does each receive?

5. A, B, and C, together, have $1200, of which A has twice, and B 3 times, as much as C; what is the interest of each for 5 years, at 6%?

6. If the interest of $2500 for 4 years, at 10 per cent., be divided into two parts, which are as 2 to 3, it will respectively give of B's and of A's money; how much has each ?

7. The interest on of A's and of B's fortune, for 5 years, at 0 per cent., is $240; what is the fortune of each, provided of A's equals of B's?

8. A's money is 4 times B's, and the sum of the interest received by both for 3 years, at 8 per cent., is $600; how much money bas each?

9. The interest for 4 years, at 5 per cent., on the money Martin owes, is $40; and the interest for the same time and rate per cent. on

the money due him, is $70; how much more has he due than he owes?

10. The interest on the money A paid for a farm, house, and store, for 8 years, at 5 per cent., equals $18000; what was the cost of each. provided the farm cost 3 times as much as the house, and the house twice as much as the store?

11 A man wishes to place such a sum of money on interest at 6 per cent., that it will give an annual interest of $360 for a poor sister; required the amount invested.

12. Two-thirds of A's fortune, plus of B's, being on interest for 6 years, at 5 per cent, amounts to $7800; what is the fortune of each, supposing of A's equals of B's?

INTEREST ON PROMISSORY NOTES.

479. A Promissory Note is a written agreement to pay some person a certain sum of money on demand, or at a specified time.

480. The Face of a note is the sum whose payment is promised. It is written in words in the body of the note, and in figures at the top.

The number of cents is usually expressed in figures as hundredths of a dollar, as is seen in the note below.

481. The Maker of a note is the party who signs it. The Payee is the party to whom it is made payable. The Holder is the one who owns it.

In the following promissory note, let the pupil point out the maker, the payee, the face, the date, etc.:

$250.25. Philadelphia, May 12, 1888. Thirty days after date, I promise to pay Henry Martin, or order, Two Hundred and Fifty Dollars, for value received, without defalcation, CHARLES MILLER.

If a note reads "with interest," it draws interest from date; otherwise it draws interest from the time of maturity until paid. A note may draw interest from a particular time after date, if so specified in the note. When no rate is mentioned, the legal rate of the State

is understood.

A note should contain the words, "value received," otherwise the holder may be required to prove that value was received. In business language a note is said to be "made in favor of" the payee.

482. A Negotiable Note is a note that can be transferred from one party to another. A note is negotiable when it is made payable to the "bearer," or to the "order" of the payee.

A note

A note payable "to order" becomes negotiable by the payee writing his name on the back of it, which is called indorsing the note. payable "to bearer" is negotiable without indorsement. A note payable to a particular person only, is not negotiable.

The words "without defalcation" are required in Pennsylvania to make a note negotiable; in New Jersey, "without defalcation or discount." 488. The Indorser of a note is the party who puts his name on the back as security for its payment.

It is customary in raising money on notes, to have one or more responsible persons write their names on the back of the note as security for its payment. In case of the refusal of the maker to pay the note when due, each indorser is liable for the whole amount of the note in the order of signing, unless he writes above his name the words "without recourse, or unless there is an agreement between two or more indorsers to share the loss between them.

When the maker fails to pay a note, it is usual for the holder to make his demand on the last liable indorser, who pays the note and then gets the amount from the preceding indorser, and so on, up to the first indorser. The holder, however, has the option of collecting the amount from any liable indorser, and when so collected, all subsequent indorsers are released, the indorser who pays becomes the holder, and may col lect from any prior liable indorser, and so on up to the first.

484. The Maturity of a note is its becoming legally due at the expiration of the time. In many of the States a note matures three days after the time specified.

485. 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.

In several of the States, as New York, Pennsylvania, New Jersey, Illinois, etc., days of grace are abolished by law.

When grace is allowed the note matures on the last day of grace. When no grace is allowed, it matures at the expiration of the time specified. If a note is payable on demand, it is legally due when presented. If a note becomes legally due on Sunday or a legal holiday, it must be paid in most States on the day preceding. In Pennsylvania it is to be paid on the next business day following; and in New York a note maturing on a legal holiday, or Monday observed as such holiday, is payable the following day. When days of grace are reckoned, the following notation indicates when a note is nominally and legally due: July 4 | 7, 1876.

When the time of a note is stated in months, calendar months are meant. A note for 4 months, dated Oct. 15, would mature Feb. 15 | 18; but if dated Oct. 29th, 30th, or 31st, it would expire on the last day of February, and be legally due on the 3d of March.

486. A Protest is a written declaration made by a notary public, that the maker of a note has failed to pay it.

A protest must be made out on the day the note matures, and sent to the indorser immediately, to hold him responsible. The neglect to protes a note on maturity releases an indorser from all obligation to pay it, un less the words "waiving demand and notice" appear above the indorser' signature. In Pennsylvania a note is not to be protested on Saturday, but on the next business day following.

There are two methods of estimating the time between different dates. The first is by compound subtraction, which is still generally used in partial payments. The second is by determining the number of entire years, if any, and then reckoning the number of days left, either by adding the number in the different months between the dates, or from the table, Art. 296. This latter method is now generally adopted by merchants in finding interest on items in an account, and for calculations for short periods, and will be used in the following examples.

487. The Principal Kinds of notes will now be given, and the calculation of the interest upon them required.

A Time Note is one made payable at a specified time; when no time of payment is specified, the note is due on demand. A Joint Note is a note signed by two or more persons who are jointly liable for its payment. A Joint and Several Note is a note signed by several persons who are both jointly and singly liable for its payment.

A Principal and Surety Note is one in which another person becomes security for the payment of the note by the maker. A surety note should be made payable to the order of the surety, who should indorse it on the back to the order of the creditor. It is held that a note made in favor of the creditor and indorsed by the surety, does not bind the latter to the payment of the debt. In reckoning the interest on notes, 3 days of grace are to be allowed.

WRITTEN EXERCISES.

1. $225.

TIME NOTE.

INDIANA, PA., Dec. 15, 1886

Two months after date, I promise to pay John H, Landis, OT order, Two Hundred and Twenty-five Dollars, with interest, for value received, without defalcation.

What will be due on this note at maturity?

R. W. FAIR.