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353. The Discount can be found by subtracting the present worth from the face of the debt.

NOTE. The discount on a sum of money obtained in this way is sometimes called true discount.

90. What is the present worth of $37.44 due in 8 months? What is the discount?

Amount of $1 for 8 m....$ 1.04) $ 37.44 ($ 36, Present worth.

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91. What is the present worth of $346.87 due in 2 yr. 4 m. 12 d. ?

Ans. $303.74-.

92. What is the discount on $ 456.25 due in 9 m. 12 d?

93. What is the present worth of $490.50 due in 1 yr. What is the discount?

6 m.?

94. What is the discount on $315 due in 1 yr. at 5 % ?

95. What is the present worth of a note for $350 due 6 months hence?

96. I have a note for $436 payable June 21, 1894. What is the worth of the note May 12, 1894, money being worth 8% per annum?

354. Principal, Interest, and Rate given, to find the Time.

97, For what time must $200 be on interest at 6 % to gain $36?

Solution. $200 in 1 year, at 6 %, will gain $12; therefore, to gain $36, the time in years must be the quotient of $36÷$123, Ans. Hence,

Rule.

Divide the given interest by the interest of the principal for one year at the given rate, and the quotient will be the time.

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98. How long must $254 be on interest at 5% to gain $ 44.45?

99. How long must $ 75 be on interest at 8 % to gain $ 15.80? 100. How long must $200 be on interest at 6 % to amount to $236?

101. For what time must $72 be on interest at 8% to amount to $87.30 ?

102. For what time must $1000 be on interest at 9% to gain $247.50?

103. How long must $ 100 be on interest at 5 % to gain $ 100? Solution. $100 in 1 year at 5 % will gain $5; hence, to gain $100, the time in years must be the quotient of $ 100 ÷ $5 = 20; that is,

To find the time in which any sum will double itself, at any rate per cent, divide 100 by the rate, and the quotient will be the number of years.

104. In how many years will $50 amount to $100 at 8% ? 105. How long will it take any sum of money to double itself on interest at 6 % ?

106. In what time will a sum of money triple itself on interest at 5% ?

355. Interest, Time, and Rate given, to find the Principal. 107. What principal at 6 % will gain $ 18 in 1 yr. 6 m.? Solution. $1, in 1 yr. 6 m., at 6%, will gain $0.09. Therefore the principal must be the quotient of $180.09 $200, Ans. Hence,

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Rule.

Divide the given interest by the interest of $1 for the given rate and time, and the quotient will be the principal.

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108. What principal at 6 % will gain $ 13 in 8 months?

109. What principal on interest at 8 % per annum will gain $150 semi-annually?

110. B endowed a professorship with a salary of $2000 per annum; what sum must he invest at 6 % to provide this salary?

PARTIAL PAYMENTS.

356. Partial Payments are payments in part of a note or other obligation.

357. A Promissory Note, usually called a Note, is a written promise to pay on demand, or at a specified time, a certain sum of money for value received.

358. The Principal, or Face of the Note, is the sum named in the note.

359. The Promisor, or Maker of the Note, is the person who signs the note.

360. The Promisee, or Payee, is the person to whom, or to whose order, the money is to be paid.

361. The Indorser of a Note is the person who writes his name on the back of a note, and thus becomes responsible for its payment.

362. Statements on the back of the note of the payments with the dates are called Indorsements.

$653.57.

Boston, Feb. 17, 1891.

or

On demand, I promise to pay James E. Torrey, order, six hundred fifty-three dollars and fifty-seven cents, with interest at 7%.

Value received.

Matthew H. Shields.

(Back of the note.)

d fifty dollars ($150).

Jan. 8, 1892.

Pec'd on within one hundred

Feb. 27, 1893,

Pec'd on within

one hundred twenty-
five dollars ($125):
Aug. 10, 1894,

Rec'd on within

two hundred fifteen dollars ($215).

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363. For finding the sum due on a note on which there are indorsements the following is

The United States Rule.

Find the amount of the principal to the time when the payment, or the sum of the payments, equals or exceeds the interest due; then subtract the payment, or the sum of the payments, from the amount of the principal, and the remainder is a new principal, with which proceed as before.

(111.)

$346.36.

BOSTON, March 26, 1892.

On demand, we promise to pay Stephen C. Jones, or bearer, three hundred forty-six and 36 dollars, with interest. Value received. BRUCE & DAVIS.

INDORSEMENTS: July 20, 1892, $54.75; April 8, 1893, $10; Sept. 26, 1893, $5.50; Jan. 6, 1894, $150.46.

What was due May 2, 1894?

Principal

Interest to July 20, 1892 (3 m. 24 d.)......................
Amount....

1st payment
New principal...

(The payment April 8, 1893, is less than the interest then due; and the sum of the payments April 8, 1893, and Sept. 26, 1893, is less than the interest due Sept. 26, 1893.)

Interest to Jan. 6, 1894 (1 yr. 5 m. 17 d.).........
Amount.

Sum of 2d, 3d, and 4th payments...

$346.36

6.581

.$352.941

54.75

.$298.191

26.191

$324.382

165.96

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NOTE. Unless the payment and the interest are very nearly equal, one can calculate mentally whether the payment exceeds the interest or not. In the example above the interest of $298.191 (the amount due July 20, 1892) is almost $18 a year, while the payment April 8, 1893, is only $10; and the sum of the payments made April 8 and Sept. 26, 1893, is only $15.50.

(112.)

$525.

CAMBRIDGE, MASS., June 4, 1889.

On demand, I promise to pay John Davis, or order, five hundred twenty-five dollars, with interest. Value received.

DANIEL FOX.

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