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375. Hence, to find the bank discount and the avails of a note, payable at a specified future time, without interest,

Rule.

Find the interest on the face of the note, at the given rate, from the time of discounting to maturity, and the result will be the discount. Subtract the discount from the face of the note, and the remainder will be the avails.

NOTE 1. When a note becomes due on Sunday or a legal holiday, it is legally payable on the preceding day.

NOTE 2. A note made payable in a certain number of days is not due until that number of days and grace expire; thus a thirty days' note, dated Jan. 31, becomes due March 5 (or, in leap year, March 4), but a note made payable in a certain number of months, nominally matures on the same day of the month that it is dated, if there are so many days in the month when it matures ; or, if there are not so many days in the month, it matures on the last day of the month; thus, a one month note, dated on the 28th of February, nominally matures March 28, and legally matures March 31 ; but a one month note, dated on Jan. 28 (except iu leap year), or on Jan. 29, Jan. 30, or Jan. 31, nominally matures Feb. 28, and legally March 3.

NOTE 3. When the time of discount is less than 2 months many banks count the exact days from discount to maturity. Thus, if a note is discounted Oct. 12, and matures Dec. 5, the time is 1 m. 23 d., but the bank computes interest for 54 days.

376. Written Exercises. 1. What is the bank discount on a 90 days' note for $ 368? What are the avails ?

OPERATION.

Interest for 60 days .............$ 3.68
16 " 30 " ...

1.84
66 " 3 "

0.184
“ “ 93 “ ............$5.704, 1st Ans.

$368 – $5.70 = $362.30, avails, 2d Ans. 2. I have a 6 months' note for $ 768, dated May 12; what will be the avails if I get it discounted Sept. 3?

Six months and OPERATION.

grace from May 12 Interest for 2 m. .........$ 7.68 expire Nov. 15.

" " 12 d........... 1.536 From Sept. 3 to Discount ..................$ 9.216

Nov. 15 is 2 m.

12 d., the time for $768 - $ 9.22 = $ 758.78, avails, Ans.

which the note is

discounted. 3. What will be the bank discount and what the avails of a 4 months' note for $ 8646 ?

4. Of a 90 days' note for $ 1842 at 7 % ? 5. Of a 6 months' note for $ 489 at 5 %?

6. A 4 months' note for $ 629, dated Feb. 27, was discounted Apr. 12; what were the avails ? '

NOTE 4. When a note bearing interest is discounted before its maturity, the amount of the note at maturity, rather than its face, is the base for discounting.

7. What are the proceeds of a note for $ 10000, payable in 6 months and bearing interest, if discounted 2 months before its maturity ?

Solution. The amount of $ 10000 for 6 m. 3 d. is $10305, and the interest of $ 10305 for 2 m. is $ 103.05, which taken from $ 10305 leaves $ 10201.95, Ans.

8. What are the avails of a note for $6844, payable in 4 months and bearing interest, if discounted 1 month after date?

377. To find the sum for which a note must be written that the avails or proceeds may be a specified sum.

9. For what sum must a 45 days' note be written that the avails may be $ 240 ?

The avails of $1 for 45 OPERATION. ,

$ 1.000

days and grace are $0.992, Interest of $1 for 48 days... 0.008

and therefore the face of

the note must be as many Avails of $1 ...............$0.992

dollars as $0.992 is con$ 240 = 0.992= $ 241.94, Ans. tained times in $ 240, or

$ 241.94. Hence,

Rule. Divide the required proceeds by the proceeds of $1 for the given rate and time, and the quotient will be the face of the required note.

10. For what sum must a 3 months' note be given, that the proceeds may be $ 300 ?

11. A farmer sold produce for which he received a 60 days' note, which he immediately had discounted at the bank. The avails of the note were $ 593.70; what was its face?

12. A merchant wishes to borrow $ 1200 at a bank, for 90 days; what shall be the face of the note, the rate of interest being 7 % ?

378. Miscellaneous Written Examples. 13. What is the bank discount of a note of $ 765.84 due in 3 months at 8 % ? $873.45.

BROOKLYN, N. Y., Sept. 17, 1878. Four months after date I promise to pay John Brown, or order, eight hundred seventy-three dollars and forty-five cents. Value received.

CHARLES STEVENS. 14. Find the proceeds of the above note if discounted on its date at a bank at 6 %.

15. Find the avails if discounted at a bank Oct. 29, 1878, at 7 %.

16. Find the avails if discounted Nov. 26, 1878, at 7} %. Find the proceeds of:

17. A 4 months' note for $ 315.70, dated June 9, discounted July 25, at 4 %.

18. A 90 days' note for $1125, dated Aug. 15, discounted Sept. 3, at 5 %.

19. A 3 months' note for $ 768.50, dated Dec. 13, 1878, discounted Jan. 22, 1879, at 5} %.

20. A 75 days' note for $ 348.56, dated March 9, discounted April 3, at 6 %. “ 21. A 6 months' note for $ 2916.80, dated Apr. 19, discounted June 26, at 4 %.

22. A 60 days' note for $ 285.75, dated Oct. 13, discounted Nov. 5, at 7 %.

23. A 5 months' note for $ 131.40, dated Sept. 30, discounted Dec. 1, at 7%.

24. A 45 days' note for $ 463.19, dated July 10, discounted Aug. 2, at 6 %.

25. A 3 months' note for $ 2500, dated July 16, discounted Aug. 22, at 8%.

26. A 4 months' note for $ 916.80, dated Mar. 20, discounted May 11, at 7 %. $ 987.44.

Boston, Oct. 25, 1878. For value received, I promise to pay William Simpson & Co., or order, nine hundred eighty-seven dollars and forty-four cents, six months from date, with interest at 8 %. Tuomas P. Fox.

27. What are the avails of the above note if discounted at date at 6 %?

28. What are the avails if discounted Jan. 1, 1879 at 6 %? 29. What is the value at maturity? 30. What is the value Sept. 13, 1879 ?

31. What must be the face of a 60 days' note discounted on its date at 6 % in order that the avails may be $ 150 ?

32. What must be the face of a 3 months' note discounted on its date at 7 % in order that the avails may be $ 316 ?

33. If at 5% discount $ 223.75 is received July 12, 1878, on a note dated June 8, 1878, and maturing Sept. 2/5, 1878, what is its face?

34. If at 73% % discount $ 75.15 is received on a 60 days' noto 20 days after its date, what is the face ?

EQUATION OF PAYMENTS.

379. Equation of Payments is the method of determining when several sums, payable at different times, may be paid at one time without loss to either debtor or creditor.

380. The equated time is the date of payment.

381. Written Exercises. 1. A owes B $ 900, of which $ 200 is due June 12, 1879, $ 300 Aug. 8, and $ 400 Sept. 19. When can A pay the $ 900 in one sum without loss to either A or B?

Interest Method.

OPERATION.

Due. Amount. Time.

Interest.
June 12, $ 200
Aug. 8, 300 1 m. 27 d. $2.85
Sept. 19, 400 3 m. 7 d. 6.47
Int. of $ 900 lm.= $ 4.50) $ 9.32

2.07 m., or 2 m. 2 d. June 12, 1879, + 2 m. 2 d. = Aug. 14, 1879, Ans. If the amounts due were all paid June 12, the debtor would lose the interest on the $300 from June 12 to Aug. 8, or $2.85, and also the interest on $ 400 from June 12 to Sept. 19, or $6.47 ; that is, by paying the $900 June 12 the debtor would lose $ 2.85 + $6.47 =$9.32. Therefore, he can equitably retain the $900 as long after June 12 as it will take it to gain $ 9.32. As $900 gains $4.50 in one month it will take it as many months to gain $.9.32 as $ 4.50 is contained times in $ 9.32, or 2 m. 2 d. 2 m. 2 d. after June 12 is Aug. 14.

NOTE 1. In finding the equated time interest may be computed from the date of the first bill or from any other date, but it is most convenient to compute the interest from the first day of the month in which the first bill is (lue, because the time for which interest is to be computed on the several bills is thereby most easily determined.

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