8. In what time will a principal gain 2 times, 3 times, or 4 times itself at 10%?

9. In what time will a principal double itself at 5%? at6%? at8%? at 12%?

10. In what time will a principal treble itself at 5%? at 10%? at 20%? at 25%?

11. The amount of a principal for a certain time at 5% is $250, and for the same time at 8% is $280; required the principal and the time.

WRITTEN EXERCISES.

1. In what time will $234 give $49.14 interest, at 6%?

Rule. Divide the given interest by the interest of the principal at the given rate for ONE year.

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

2. In what time will $750, at 6 per cent., give $105 interAns. 2 yr. 4 mo.

est? 3. In what time will $720, at 6 per cent., give $957.60 amount? Ans. 5 yr. 6 mo. 4. In what time will $960, at 5 per cent., give $54.40 interest? Ans. 1 yr. 1 mo. 18 da. 5. In what time will $1800, at 4 per cent., give $3047.40 amount? Ans. 15 yr. 4 mo. 24 da. 6. In what time will $26.50, at 7 per cent., give $17.46 interest? Ans. 8 yr. 9 mo. 12 da. 7. In what time will $18.20, at 5 per cent., give $10.23 interest? Ans. 9 yr. 9 mo. 9 da. 8. The amount of a certain principal, in a certain time, at 5 per cent., is $833, and the amount for the same time at 12 per cent. is $1047.20; required the principal and time.

Ans. Prin. $680; Time, 4 yr. 6 mo. SUG.-The difference of the amounts equals the interest at 7%.

C*

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 rate.

MENTAL EXERCISES.

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

SOLUTION.-For 5 years at one per cent. 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. ?

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 $14.681 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 $7.062 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, 81%.

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 6 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 has 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. ou

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?

13. of the cost of Bowman's house, plus of the cost of his farm, being on interest for 5 years, at 8 per cent., amounts to $2100; what is the cost of each, provided the house cost as much as the farm? 14. Two times the value of a horse, plus 3 times the value of a cow, which is of the value of the horse, in 8 years, at 5%, gives $84 interest; required the value of each.

15. The money Henry paid for a horse, carriage, and harness, in 10 years, at 5 per cent., would give such an interest that if put on interest for the same time and rate, it would amount to $270; how much did he pay for each, if the horse cost twice as much as the carriage, anc the carriage 3 times as much as the harness?

INTEREST ON PROMISSORY NOTES.

479. A Promissory Note is a written promise to pay some one 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 or bottom.

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.

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. In business language a note is said to be "made in favor of" the payee.

A note should contain the words, "value received," otherwise the holder may be required to prove that value was received.

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. ble to a particular person only, is not negotiable.

A note paya

The words "without defalcation" are required in Pennsylvania to make a nože negotiable; in New Jersey, "without defalcation or discount." 483. 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 most of the States a note matures three days after the time specified, unless the words "without grace" are inserted.

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.

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 Connecticut, three days' grace is allowed on notes for $35 or more, but not on notes for a less amount; if the last day is a legal holiday falling on Sunday, the note is due on Monday. In Maine and Nebraska, if the third day is a legal holiday falling on Monday, the note is payable on Tuesday; and in New York a note maturing on a legal holiday, or Monday observed as such holiday, is payable the following day. The following notation indicates when a note is nominally and legally due: July 4|7, 1876.