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This note was presented at bank for discount April 1, 1897. Find: 1. The day of maturity. 2. The time to run. 3. The discount. 4. The proceeds.

Process.

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Feb. 26, 1897 + 3 mo. = May 26, 1897, the day of maturity.

Day of maturity, 1897 5 26
Day of presentation, 1897 4 1

1 mo. 25 da., time to run.

2360 x .06 x 55 Discount for 55 da. =

$21.64.

360
Face of note $2360.00
Discount

21.64 Proceeds $2338.36 That is, the bank took the note and paid in cash for it $2338.36.

Hence the brief directions are :
1. Find the day of maturity.
2. Find the time to run.
3. Find the discount (simple interest).
4. Find the proceeds (subtract discount from face).

EXERCISES.

.

Find the discount and proceeds of:

1. $350 for 30 da. at 5%.
2. $400 for 90 da. at 6%.
3. $540 for 60 da. at 7%.
4. $600 for 60 da. at 8%.
5. $2000 for 3 mo. at 10%.
6. $80.60 for 90 da. at 51%.
7. $5000 for 18 da. at 63 %.
8. $780 for 40 da. at 73%, with grace.
9. $600 for 2 mo. 12 da. at 81%, with grace. .
10. $1000 for 90 da. at 10%, with grace. .

PROBLEMS.

Apply the brief directions to the following notes :

(1.) $5001000

San Francisco, CAL., Feb. 20, 1898.

Sixty days after date, I promise to pay James Warner, or order, Five Hundred Dollars, value received:

JOHN GORDON. Discounted Mar, 15, 1898, at 7%.

(2.) $800,000

BALTIMORE, MD., Feb. 1, 1898. Ninety days after date, I promise to pay to the order of Peter Welsh Eight Hundred Dollars, for value received.

HENRY BRYCE. Discounted April 1, 1898, at 6%.

(3.) $400-80%

PHILADELPHIA, PA., Jan. 5, 1898.

Ninety days after date, I promise to pay Charles Garrett, or order, Four Hundred Dollars at the Girard Bank, for value received, without defalcation.

JOHN WATERMAN. Discounted Jan. 10 at 6%.

(4.) $4651700

WASHINGTON, D. C., April 20, 1898.

Six months after date, for value received, I promise to pay Alfred Rickert, or order, Four Hundred Sixty-five 76 Dollars, at the First National Bank.

WESLEY EVANS. Discounted June 23 at 7%.

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5. Find the bank discount of a note for $3600, dated March 6, 1898, and payable 3 mo. after date, with interest at 5%, if discounted May 13, 1898, at 6%.

6. Find the proceeds of a note for $2400, dated Aug. 26, 1898, payable 90 days after date, with interest, at 53%, and discounted Oct. 1, 1898, at 6%.

To find the Face of a Note.

It is sometimes necessary to determine what face to give a note in order to secure a certain sum as proceeds.

Find the face of a note that, discounted for 60 days at 6%, will yield $500 as proceeds. Process.

Explanation. Discount of $1.00 =.01.

Since $1.00, as face,

discounted for 60 da. Proceeds of $1.00 = 1.00 —.01 =.99.

at 6%, yields $.99, $500 = .99 = $505.05.

the question is, How many dollars as face will yield $500 as proceeds ? Obviously, $500 = .99

$505.05.
Hence the formula :

Face Given Proceeds + Proceeds of $1.00.
Face = Given Discount · Discount of $1.00.

EXERCISES.

Find the face in each of the following instances :

1. Proceeds, $800; time 60 da. ; rate, 6%.
2. Proceeds, $989.50; time, 2 mo.; rate, 6%.
3. Proceeds, $3000; time, 90 da. ; rate, 6%.
4. Proceeds, $15,000; time, 2 mo.; rate, 7%. Grace.
5. Proceeds, $240; time, 3 mo.; rate, 5%. Grace.
6. Proceeds, $975; time, 2 mo.; rate, 7%. Grace.
7. Discount, $40; time, 90 da. ; rate, 6%.
8. Discount, $4.18; time, 60 da. ; rate, 6%.

9. Discount, $8.48; time, 60 da. ; rate, 5%.
10. Discount $17.50; time, 2 mo. 12 da.; rate, 7%.

PROBLEMS.

1. I wish to borrow $400 at a bank. For what sum must I draw my note, payable in 60 da., so that when discounted at 6% I shall receive the desired sum ?

2. What is the face of a note at 60 days which yields $780 when discounted at a bank? Rate, 5%.

3. Suppose you buy goods in Philadelphia to the amount of $1248.50, and give your note in payment drawn at 6 mo. What must be the face of the note?

4. For how large a sum must a note be drawn, payable in 3 mo., that the net proceeds may be $7500 after deducting the bank discount at 8%?

5. A Chicago merchant sold goods, and received in payment for them a 6-mo. note, which he had immediately discounted at 7%. If he received $1898 in cash for the note, for what sum had he sold the goods?

6. For what amount must a note be made payable in 3 mo., so that when discounted in Baltimore at the legal rate (6%), the proceeds may be $1420.

7. For what sum must a note be drawn, payable in 3 mo., so that when discounted in Montana at the legal rate (10%), the proceeds may be $1000 ?

8. In Oregon I suffered a discount of $6.18 on a 6-mo. note at the legal rate (8%). Find the face of my note ?

TRUE DISCOUNT. 1. The Present Worth of a debt is a sum which, put at interest, amounts to the debt when due.

2. True Discount is the difference between the present worth and the debt. Finding the present worth is the same as finding what principal will in a given time, and at a given rate, amount to a given sum.

Amt. Hence we have, from page 256, Pr. =

which

R. X yr. +1' becomes :

P. W.

Amt. or Debt
R. X yr. + 1.

MODEL SOLUTION.

What present worth, or principal, will amount to $1000 in 8 mo. at 6% ? Also, find the true discount.

Process.
Amt.

$1000 $1000 P. W.

$961.54. R. X yr. + 1 .06 x 3+1 1.04 $1000 - $961.54 = $38.46, true discount.

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Amt

Explanation. Since the P. W. stands to the Amt. in the relation of principal, we use the formula, P. W.

and obtain $961.54. $1000 --- $961.54

R. X yr. + 1 $38.46, true discount.

Or, we may say: $1.00 amounts to $1.04; therefore, it will require the quotient of $1000 — 1.04 to amount to $1000. Hence the P. W.=$961.54.

.

EXERCISES.
Find the present worth and true discount of:

1. $400, due 1 yr. hence, at 6%.
2. $200, due 11 yr. hence, at 6%.
3. $180, due 1 yr. 5 mo. hence, at 5%.
4. $600, due 2 yr. 3 mo. hence, at 8%.
5. $350, due 2 yr. 6 mo. 9 da. hence, at 7%.
6. $1500, due 2 mo. 21 da. hence, at 5%.
7. $2000, due 2 yr. 3 mo. 6 da. hence, at 6%.
8. $487.75, due 3 yr. hence, at 7%.
9. $422.00, due 21 yr. hence, at 6%.
10. $479.373, due 3 yr. hence, at 5%.

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