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3. The account-books of L. F. Wilson and S. P. Allen show

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What is the equated time for payment?

4. When was the balance of the following account due? John H. Arnold in account with W. C. Burlingame. Cr.

Dr.

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5. What was due on the following account July 1, 1858, interest being reckoned at 6 per cent?

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121. To find the Principal or the Interest when the Amount, Rate, and Time are given.

1. What sum of money will amount to $367.65 in 1 year, at 74 per cent?

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Since, at the given rate, the interest for 1 year must equal

3

43

of the principal, the amount must equal 13, or

40

40

* i. e. on 6 mo. credit, 4 mo. credit, etc.

times the principal. Hence, the principal must equal 48 of the amount, or 48of $367.65 = $342.

2. What principal will amount to $252.791 in 1 yr. 3 mo. 18 da. at 6 per cent, and what is its interest for that time?

78 6000 1000

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SOLUTION.Since, at 6 per cent per year, interest for 1 yr. 3 mo. 18 da., or 468 days, is 468 of the principal, the amount must equal 178, or 1978 times the principal. Hence, the principal must equal interest must equal 78 of the amount. 1000 of $252.791 principal; 7 of $252.791

78 1078

1078

1078

=

=

$18.291 interest.

1000 1078'

and the

=

$234.50

=

3. The amount of a certain sum for 1 yr. 5 mo. 15 da., at 5 per cent, is $1855.545. What is the principal and what the interest?

360

360

96

SOLUTION. Since, at 5 per cent per year, interest of any sum for 1 yr. 5 mo. 15 da., or 525 days, or 35 of a year, is 525 of 180 of the prin cipal, the amount must equal 17 or 103 times of the principal. Hence, the principal must equal, and the interest must equal of the amount. 96 of $1855.545 : $1729.44 principal; of $1855.44

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(a.) From these solutions, it appears that, to find the principal or the interest when the amount, rate, and time are given, we find the fraction which expresses what part interest for the given time at the given rate is of the principal, and divide the given amount by 1 plus this fraction.

NOTE. The above-named fraction will always be the same part of the given annual rate that the given time is of 1 year, or of 360 days; or, if the rate is 6 per cent, it will equal the fraction expressing the part which the given time is of 200 months, or of 6000 days.

(b.) To find the interest, we subtract the principal, found as before, from the amount; or, we multiply the given amount by the fraction which shows what part interest for the given time and rate is of the amount.

What principal will amount to

4. $342.40 in 1 yr. 2 mo. at 6 per cent?
5. $486.404 in 8 mo. 16 da. at 6 per cent?
6. $500.55 in 2 yr. 5 mo. 5 da. at 7 per cent?
7. $1834.24 in 11 mo. 15 da. at 4 per cent?

8. $305.207 in 3 yr. 3 mo. 3 da. at 9

per

cent?

9. $490.912 in 8 mo. 8 da. at 31% per cent?
10. $363.48 in 1 yr. 4 mo. 20 da. at 6 per cent?

122. Discount and Present Worth.

(a.) Discount is an allowance made for the payment of money

before it is due.

(b.) The PRESENT WORTH of a debt due at a future time is the sum which it is supposed to be worth now.

(c.) According to the principles involved in simple interest, the present worth of a debt due at a future time is that sum of money which, put on interest now, will amount to the given debt at the time it becomes due. Hence, the given debt corresponds to the amount, the present worth to the principal, and the discount to the interest; and the problems in this article are merely additional applications of the principles involved in the last.

1. What is the present worth of $470.12, due in 1 yr. hence, at 9 per cent?

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4 mo.

SOLUTION. The present worth required is that sum of money which, put on interest at 9 per cent, will amount to $470.12 in 1 yr. 4 mo. Since, at 9 per cent per year, interest for 1 yr. 4 mo. or 16 mo. equals 9 of 9 per cent, equals 12 per cent of the principal, the amount must equal 112 per cent of the principal, and the principal, which is the present worth required, must equal 1 of the amount. But of $470.12 $419.75 worth. PROOF. The amount of $419.75 at 9 per cent. for 16 mo. = given debt.

What is the present worth of

=

=

present

$470.12

=

2. $1453.20 due in 2 yr. 9 mo. 20 da. at 6 per cent?

3. $465.26 due in 1 yr. 4 mo. 12 da. at 6 per cent?

4. $634.827 due in 2 mo. 15 da. at 8 per cent?

5. $600 due in 60 da. at 6 per cent?

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11. What is the discount of $997.542 due in 2 mo. 12 da. hence, at 7 per cent?

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SOLUTION. The discount required is the interest of that sum of money which, at 7 per cent, will amount to $997.542 in 2 mo. 12 da. Interest for 71 2 mo. 12 da., or 18 of a year, at 7 per cent, equals of of the principal; hence, the amount must equal 203 of the principal, and the discount must equal of the amount, equal to $14.742.

5 100

=

200

NOTE. The discount might have been found by finding the present worth and subtracting it from the given debt.

What is the discount of—

12. $507.50 due in 3 mo. at 6

per cent?

13. $469.464 due in 6 mo. 20 da. at 6 per cent?

14. $594.615 due in 1 yr. 1 mo. 10 da. at 6 per cent?

15. $253.46 due in 1 yr. at 6 per cent?

16. $825.14 due in 7 mo. 19 da. at 6 per cent?

17. $824.36 due in 5 mo. 17 da. at 6 per cent?
18. $927.41 due in 2 yr. at 41 per cent?

19. $683.76 due in 3 yr. at 3 per cent?
20. $437.26 due in 1 mo. 23 da. at 9 per cent?

123. Business Method of Discount.

(a.) Merchants and business men are usually willing to allow a larger rate of discount than that obtained by the method of the preceding article. Sometimes they deduct the interest of the entire debt for the time it has to run, as is always done on notes discounted at bank (see 117), and sometimes they deduct a still larger sum.

1. What will be received on a debt of $1000 due in 2 mo., discount being allowed at the rate of 6 per cent per year?

ANSWER.-$1000 minus the interest of $1000 for 2 mo. =

$990.

2. How much money will be required to pay a note of $800 due in 3 mo., discount at 6 per cent per year being allowed? *

3. Bought goods to the amount of $1200, for which I can pay either by giving my note payable in 6 mo., or by cash at a discount of 6 per cent per annum. How much shall I gain by borrowing enough money to pay for them now, and then paying the borrowed money with interest at the time when the note would have become due?

4. What is the difference between the present worth of a debt of $2000 due in 6 mo. and the sum which would be received on it, if discount be reckoned as in this article, money being worth 6 per cent per year?

5. I bought goods to the amount of $1500, payable in 4 mo.; but the seller offering to deduct 5 per cent of the debt for cash, I hired money enough to pay for them. At the end of the 4 mo., I paid the borrowed money with interest at 6 per cent. What did I gain by hiring the money?

SOLUTION.5 per cent of $1500

=

$75

discount. $1500

$75 = $1425 = sum borrowed. Amount of $1425 for 4 mo. = $1453.50, and $1500 $1453.50

=

$46.50.

6. For how much can a debt of $695.34, due in 5 mo., be paid if a discount of 8 per cent of the debt be allowed for cash?

7. I bought a note for $2500 due in 4 mo., at a discount of 5 per cent. Allowing that money was worth to me 6 per cent per year, and that the note was paid when due, how much did I gain by the transaction?

8. I sold my note for $1000 due in 2 mo., at a discount of 11⁄2 per cent per month. How much did I receive for it?

*Observe that grace is always to be allowed on notes on time.

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