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At what rate %
70. Will $ 250 gain $3.75 in 4 mo. ?
71. Will $ 25 gain $ 7.873 in 3 y. 6 mo. ?
72. Will $ 100 gain $ 25 in 77 y.?

73. The amount of $75 for 2 y. 6 mo. was $78.75; whæi was the rate % ? NOTE. To find the interest, deduct $75 from $78.75.

74. A note of $ 50 on interest from Feb. 29, 1872, to Feb. 28, 1874, amounted to $55.25; what was the rate %?

75. When a note of $1000 amounts to $ 1058.33} in 7 mn., what is the rate %?

To find the Principal, having the Interest or Amount, the

Time, and the Rate given. 567. ILLUSTRATIVE EXAMPLE I. What principal on interest at 6% for 3 y. 4 mo. will yield $ 80 of interest ?

WRITTEN WORK.

Explanation. — The interest of $1 at 1 x 0.06 x 3} = 0.20 6% for 3 y. 4 mo. is $0.20. $ 80.00 - $ 0.20 = 400

Since 1 dollar of principal at 6% in 3 y. Ans. $ 400.

4 mo. yields 20 cents of interest, to yield

$ 80 of interest will require as many dollars of principal as there are times 20 cents in $ 80, which is 400. Ans. $ 400.

568. ILLUSTRATIVE EXAMPLE II. What principal on interest at 10% for 2 y. 6 mo. will amount to $ 478.50 ?

Explanation. The interest of $ 1 1 x 0.10 > 2} = 0.25 for 2 y. 6 mo. at 10% is $0.25, and the $1.25) $478.50 (382.8

amount of $1 is $ 1.25. 375

Since $1 of principal at 10% in 2 y.

6 mo. amounts to $ 1.25, to amount to 1035

$478.50 will require as many dollars 1000

of principal as there are times $ 1.25 350

in $478.50, which is 382.8. 250

Ans. $ 382.80

WRITTEN WORK.

1000 etc.

569. From the foregoing may be derived the following

Rules.

I. To find the principal, having the interest, the time, and the rate given: Divide the given interest by the interest of $1 for the given time and rate.

II. To find the principal, having the amount, the time, and the rate given: Divide the given amount by the amount of $1 for the given time and rate.

The above rules may be expressed by the formulas :

Interest 3. Principal

Rate x Number of years

Amount 4. Principal =

1 + Rate x Number of years

570. Examples for the Slate. What principal on interest 76. At 6% will gain $ 15 in 2 years ? 77. At 5% will gain $20 in 4 years ? 78. At 3% will gain $ 76.50 in 2 y. 6 mo. ? 79. At 4% will gain $ 1.705 in 7 mo. 15 d. ? 80. At 6% will gain $4.128 in 11 mo. 14 d. ?

NOTE. 4.128 = 0.057} (both changed to thirds of thousandths) equals 12.384 ; 0.172.

81. At 2% a month will gain $ 24 in 60 days ?
82. At 6% will amount to $870 in 7 y. 6 mo. ?
83. At 5% will amount to $ 2072.25 in 30 d. ?
84. At 1% a month will amount to $ 412 in 90 d. ?

85. What sum on interest 3} yrs. at 54% vill amount to $ 100 ?

86. What sum put upon interest Jan. 1, 1875, at 7% will amount to $ 343.75, Feb. 1, 1877 ?

87. What principal put upon interest to-day at 5% will amount to $ 206.25 in 7 mo. 15 d. ?

PRESENT WORTH AND DISCOUNT.

WRITTEN WORK.

571. ILLUSTRATIVE EXAMPLE. If one person owes another $ 214, to be paid 1 year hence, without interest, what sum should be paid to-day to discharge the debt, the current rate of interest being 7 per cent ?

Explanation. - In justice to both parties, 1.07) 214.00 (200

such a sum should be paid to-day as would, 214

if put at interest at 7%, in 1 year amount to

$ 214. Ans. $ 200.

Since $1 in 1 year at 7 % amounts to $1.07, it would require as many dollars to amount to $ 214 as there are times $ 1.07 in $214, which is 200. Ans. $ 200.

572. A sum which will without loss to either party discharge a debt at a given time before the debt is due is the present worth of the debt.

573. A sum deducted from a debt or from a price is discount. The difference between the face of a debt and the present worth is the true discount.

What is the present worth in the example above ? What is the true discount?

NOTE. — It will be seen that the present worth is the principal, the true discount is the interest, and the sum due at a future time is the amount. This subject is then an application of that illustrated in Art. 568.

574. From the illustrative example above may be derived the following

Rules. 1. To find the present worth: Divide the given debt by the amount of $1 for the given time and rate.

II. To find the true discount: Subtract the present worth from the face of the debt.

page 333

PRESENT WORTH AND DISCOUNT.

225

575. Examples for the Slate.

The current rate of interest being 6%, what is the present worth and what is the true discount

88. Of $ 27.50, due 1 year 8 months hence ?
89. Of $ 100.96, due 8 months hence ?
90. Of $ 200, due in 3 months ?
91. Of $ 175.80, due in 9 months 20 days?
92. Of $ 661.37], due in 3 months 15 days?

93. What is the present worth and true discount of $ 1609.30, due in 10 months 24 days, current rate 5% ?

94. If a bill of $600 is payable in 3 months after May 1, without interest, what sum will discharge it June 1, current rate of interest being 10% ?

95. Macomber & Earle sold goods to the amount of $138.48 on 6 months' credit. For how much ready money could they afford to sell the same goods, the use of the money being worth to them 2% a month?

96. A merchant bought goods to the amount of $1574, one half payable in 3 months and the rest in 6 months, without interest. What sum would pay the debt at the time of purchase, rate 7%?

97. A dealer bought $ 1500 worth of grain on 6 months' credit, and sold it immediately for 10% advance. If with the proceeds he paid the present worth of the $1500, rate 8%, what sum remained ?

98. A bookseller bought $ 240 worth of books at a discount of 33} % on the amount of his bill, and 5% on the balance for present payment. He then sold the books on 3 months' time for the price at which they were billed to him. Money being worth 7 %, and the purchaser discounting his own bill by true present worth at the time of purchase, what was the bookseller's gain ?

For other examples in present worth, see page 253.

BANK DISCOUNT.

576. Holding a note against James Peak for $ 500, dated April 1, and given for 4 months, without interest, and desiring the money April 1, I transfer the note to a bank, and allowing the bank to take interest on the sum named in the note for 4 months, and 3 days ($ 10.25), receive from the bank the balance ($ 489.75) in cash. The note is then said to be discounted.

The sum named in the note is called the face of the note.

Before transferring the above note, I endorsed it by writing my name across the back and thus became responsible for the payment of the note when due.

577. The three days for which interest is taken beyond the specified time for paying a note are called days of grace.

Note I. A note is nominally due at the expiration of the time specified in the note, but it is not legally due till the expiration of the 3 days of grace. A note is said to mature when it is legally due.

578. The interest upon the face of a note from the time it is discounted to the time it matures is bank discount.

What is the bank discount in the example given ?

579. The face of a note, less the discount, is the proceeds, avails, or cash value of the note.

What are the proceeds in the example given ?

Note II. The time when a note is nominally and when legally due is usually written with a line between the dates; thus, August 1/4.

Note III. When a note is given for months, calendar months are understood, and the note is nominally due on the day corresponding with its date ; if the month in which it falls due has no corresponding day it is due on the last day of that month.

NOTE IV. Notes maturing on Sunday or on a legal holiday must be paid on the business day next preceding.

Note V. In computing bank discount, the more general custom is to reckon the time in days; hence, in the examples in bank discount which follow, the time is so reckoned, when dates are given

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