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6. $600.

READING, PA., Dec. 14, 1887. Three months after date, I promise to pay Mary Smith, or or der, at the First National Bank, Six Hundred Dollars, with inter. est, for value received, without defalcation.

JOAN SMITH. What was the value of this note at maturity? Ans. $609.10.

ANNUAL INTEREST. 488. Annual Interest is the simple interest of the prin. cipal, and of each year's interest from the time of its accruing until settlement.

489. Annual Interest is sanctioned by some States when the note is written“ with interest payable annually.”

1. Simple Interest is not due, and cannot be collected until the princi. pal is due, unless the note reads, “with interest payable annually." Annual Interest allows interest on the unpaid interest of a debt as well as upon the debt itself.

2. In Compound Interest, each year's interest is added to the principal, and the sum forms a new principal for the succeeding year.

3. The neglect to collect the annual interest on a note drawn with interest payable annually," is in some States, regarded as a waiving of the contract requiring it.

1. What is the amount due on a note of $300, at 6% for 3 yr. 3 mo., interest payable annually?

SOLUTION.-The interest on $300 for one year

$18, and
$300 x .06= $18

int, for lyr.
for 3 yr. 3 mo. is $58.50; the
first year's interest

on inter

$18 x 34 58.50, int. for 34 yr. est 2yr. 3 mo., giving $2.43 in

$18 X.135= 2.43, int, on 1st int. terest; the second year's is on

$18 X.075= 1.35, int, on 2d int. interest for 1 yr. 3 mo., amount

$18 X.015 = .27, int on 3d int. ing to $1.35; the third year's

300.00 principal. interest is on interest 3 mo.,

$362.55 amounting to $.27; adding the interest on the principal, the interest on each year's interest, and the principal, we have $362.55 as the amount due.

Rule.-I. Find the interest on the principal for the given time and rate : also find the interest on each year's interest for the time it has remained unpaid.

II. The sum of these interests will be the annual interest, and this, added to the principal, will be the amount due.

OPERATION.

NOTR.—The work may be shortened by calculating the interest for the sum of the times during which the different interests remain unpaid.

WRITTEN EXERCISES. 2. What is the interest due on a note for $840, dated March 2, 1872, interest payable annually, if no payments are made till Sept. 9, 1876 ?

Ans. $252.90. 3. How mucb is due Jan. 1, 1877, on a note for $1000, dated June 16, 1873, interest payable annually at 7%, if ibe yearly interest bas been regularly paid ? Ans. $1038.69 4. $1250.

CONCORD, N. H., Feb. 10, 1871. For value received, I promise to pay to the order of Jacob Clark, on demand, One Thousand Two Hundred and Fifty Dollars, with interest annually. THOMAS MAYNARD.

What was due on this note, June 11, 1875, if the annual interest was paid up for the first two years ?

Ans. $1432.73. PARTIAL PAYMENTS. 490. Partial Payments are payments in part of notes or other obligations bearing interest.

491. An Indorsement is an acknowledgment of a pay ment written on the back of the obligation, stating the time and amount of the payment.

The term Indorsement is used in different business papers, in each case, however, meaning a writing on the back, from the Latin dorsum, the back.

1. The writing of the name on the back of a check, draft, note, etc., is called a General Indorsement. or an indorsement in blank.

2. A Special Indorsement uirects the obligation to be paid to some par cicular person, or to his order.

3. An acknowledgment of the payments on a note, written on the back of it, is also an indorsement. The person holding the obligation signs his name to this statement as a receipt.

492. The Supreme Court of the United States, and nearly all the States, adopt the following rule for partial payments, called

THE UNITED STATES RULE. I. Find the amount of the principal to the time of the first payment; if the payment equals or excecds the interest, subtract the payment from the amount and treat the remainder as a new principal.

II. If the payment is less than the interest, find the amount of the same principal to the time when the sum of the payments shall equal or exceed the interest due, and subtract the sum of the payments from the amount.

III. Proceed in the same manner with the remaining payments until the time of settlement.

Note. This rule is founded upon the decision of Chancellor Kent. The principle is, that neither interest nor payment shall draw interest. It has been adopted by nearly all the States-New Hampshire, Vermont, and Connecticut being the principal exceptions. 1. $600

MILLERSVILLE, PA., July 12, 1870. Four years after date, I promise to pay Henry Wilson, or order, Six Hundred Dollars, with interest, for value received

CHARLES HARDING. On this note were the following indorsements : May 24, 1871, received .

$131.20 Dec. 18, 1872,

40.00 Sept. 12, 1873,

175.00 How much remained due July 12, 1874 ?

18741

OPERATION.

Principal, or face of note

$600.00 Interest to first payment

31.20 Amount due May 24, 1871

631.20 First payment to be deducted

131.20 Balance due after first payment

500.00 Interest on balance to second payment is $47.00. The pay:

ment being less, is not deducted. Interest from first payment to third payment

69.00 Amount due Sept. 12, 1873

569.00 Sum of second and third payments to be deducted :

216.00 Balance due after third payment

354.00 Interest from Sept. 12, 1873, to July 12, i874

17.70 Balance due on settlement, July 12, 1874

371.70 . $4600

LANCASTER, PA., May 10, 1870. Five years after date, for value received, I promise to pay Robert Turner, or order, Four Thousand Dollars, with interest from date.

MORTON BLACK, Jan. Indorsements: May 10, 1871, $300; May 22, 1872, $250; June 16, 1873,

$70; July 30, 1874, $175. How mucb was due May 10, 1875? Ans. $4389.58.

8. $800.

COLUMBIA, PA., March 10, 1870. For value received, on demand, I promise to pay W. A. Fisher, Eight Hundred Dollars, with interest.

W. H. CROTHERS. Indorsements: Feb. 16, 1871, $10.00; Oct. 20, 1871, $75.00; Jan. 14.

1872, $15.00; April 26, 1872, $10.00. The note was settled Sept. 1, 1872; what was then due?

Ans. $808.25. 4. A note of $7000 was given Jan. 1, 1872. Indorsements: May 3, 1873, $400; Aug. 8, 1874, $70; Sept. 9, 1875,

$120; Oct. 7, 1876, $950. What was due Jan. 1, 1877, Int. 7%? Ans. $7910.

5. A note of $5860 was given Sept. 10, 1874. Indorsements: Aug. 16, 1875, $150; May 18, 1876, $350; Dec. 28, 1877,

$95; Nov. 17, 1878, $112. What was due Jan. 1, 1879, Int. 5%? Ans. $6414.66.

6. A note of $3500 was given May 12, 1870. Indorsements: Jan. 16, 1871, $50; July 10, 1871, $25; Dec. 18, 1871,

$250; June 20, 1872, $475; Aug. 20, 1873, $75; Sept.

30, 1873, $35. What was due Jan. 1, 1874, Int. 6% ? Ans. $3320.72.

493. Business men generally settle notes and interest accounts, payable within a year, by the following rule, called the

MERCHANTS' RULE. I. Find the amount of the principal to the time of settlement, and also the amount of each payment to the time of settlement.

II. Subtract the sum of the amounts of the payments from the amount of the principal, for the balance due.

NOTES.-1. In some States merchants apply this rule to notes for longer periods by reckoning the interest for 1 year, and subtracting from the amount the amounts of the payments made during the year,

and taking this balance for a new principal.

2. As the periods in these notes are all short, the interest 'should be cal. eulated for the number of days. 1. $5480.

PHILADELPHIA, Jan. 1, 1875. Sixty days after date, for value received, I promise to pay Joseph Trotter, or order, Five Thousand Four Hun dred and Eighty Dollars, without defalcation.

JAMES TAYLOR. Indorsements: March 15, $200; June 12, $300; Aug. 9, $500; Oct. 1,

$700. What is due Dec. 3, 1875?

Ans. $3997.60. 2. A note of $4774.25 was given Nov. 9, 1875. Inchorsements: Jan. 1, 1876, $500; Feb. 12, $600; April 17, $450;

Jun 10, $247.50; Aug. 1, $250. What is due Oct. 1, 1876, at 7%? Ans. $2953.592.

3. A note was given for $1250, April 20, 1874. Indorsements: May 10, $200; July 17, $50; Sept. 25, $140; Oct. 19

$150; Dec. 12, $350. What was due April 20, 1875, at 5%? Ans. $396.89.

NOTE.-For Connecticut, Vermont, and New Hampshire rules, see Brooks's Higher Arithmetic.

DISCOUNT AND PRESENT WORTH. 494. Discount is an allowance made for the payment of money before it becomes due.

495. The Present Worth of a debt payable at a future time without interest is such a sum as, being on interest tor the time at a certain rate, will amount to the debt.

496. The True Discount is the difference between the amount of the debt and the present worth.

NOTES.-1. The true discount is the interest on the present worth for the time between the payment of the debt and the time it becomes due.

2. The present worth corresponds to the principal, the discount to the interest, and the debt to the amount; hence the different cases may be solved as in Interest.

1. What is the present worth of $585, due 5 years hence without interest, money being worth 6% ? SOLUTION.--The amount of $1 for 5 years,

OPERATION. at 6%, is $1.30, hence the present worth of

$0.06 X 55$0.30 $1.30 is $1, and the present worth of $585 is

Amount=$1.30 as many times $1 as $1.30 is contained times $585:-1.30–$450, Ans. in $585, which is $450. Hence

Rule.-I. Divide the given sum by the amount of $1 for the given rate and time, to find the present worth.

I Subtract the present worth from the given sum to find the discount.

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