10. I wish to send a sight bill of exchange on Berlin in payment of the following invoice:

4 cases musical instruments amounting to 3,598.60 marks, less 10, 5, and 21%.

Freight to Hamburg, 165 kilos, at 4.80 marks per kilo.

At 95 for 4 marks, what will be the cost of the bill of exchange?

CHAPTER XIII.

PARTIAL PAYMENTS.-RATIO AND PROPORTION.-SQUARE ROOT. SURFACES AND VOLUMES.

1008. U.S. Rule.

PARTIAL PAYMENTS.

DULUTH, MINN., Jan. 5, 1889.

On demand, I promise to pay to the order of Owen McGee Three Hundred Dollars, value received, with interest at 7 per

cent.

$300,00

100.

J. RANDOLPH PAGE.

Endorsements: May 20, 1889, $100; Oct. 30, 1889, $100; March 6, 1890, $50.

How much was due Jan. 5, 1891?

Find amount of $300 Jan. 5, 1889, to first payment May 20, 1889, 4 mo. 15 da. (by compound subtraction).

Deduct first payment,

Balance May 20, 1889,

$307.88

100.00

$207.88

Amount,

Balance Oct. 30, 1889,

Interest on $114.35 Oct. 30 to March 6, 4 mo. 6 da.,

Less third payment,

Balance March 6, 1890,

Interest on $67.15 March 6 to Jan. 5, 9 mo. 29 da.,

Due Jan. 5, 1891,

$114.35

2.80

$117.15

50.00

$67.15

3.90

$71.05

1. How much is due June 3, 1896, on a demand note for $1,200, with interest at 6%, dated June 3, 1893, bearing endorsements of payment of $500, Sept. 18, 1894; $600, Jan. 3, 1895?

2. A demand note for $600, bearing interest at 5%, was given Feb. 18, 1892. A payment of $250 was made May 28, 1893; one of $150 was made Oct. 8, 1893. How much is due Jan. 23, 1895?

3. Note for $2,000; interest, 7%; dated April 15, 1891. Endorsements: $50, Sept. 20, 1891; $100, May 26, 1892; $1,000, June 20, 1893. How much is due Dec. 27, 1894?

1010. Face of note,

Interest from April 15 to Sept. 20, 1891, 5 mo. 5 da.,
Amount due Sept. 20, 1891,

If the $50 payment were deducted, and interest computed on the balance, $2,010.27, the maker would be charged interest on $10.27 more than the face of the note, and this the law does not allow. Interest is taken on $2,000 until next payment, May 26, 1892, 8 mo. 6 da.,

Amount due May 26, 1892,

As the two payments are not large enough to meet the interest now due, the interest is again calculated on the original $2,000 from May 26, 1892, to June 20, 1893, 1 yr. 24 da.,

Amount,

Less $50 + $100 + $1,000 (three payments),

Balance due June 20, 1893,

Interest on $1,155.26 to Dec. 27, 1894, 1 yr. 6 mo. 7 da.,
Due Dec. 27, 1894,

$2,000.00

60.28 $2,060.28

95.67 $2,155.95

149.33 $2,305.28

1,150.00

$1,155.28

122.87

$1,278.15

1011. By the United States rule for partial payments, the amount of the principal is found to the time when the payment, or the sum of two or more payments, equals or exceeds the interest. From this amount deduct the payment or sum of payments. Use the balance then due as a new principal, and proceed as before.

4.

ALBANY, N.Y., March 5, 1893.

One year after date, I promise to pay John Harrigan, or order, Nine Hundred Dollars, value received, with interest at six per cent.

$900,00%

ANDREW T. SULLIVAN.

Endorsed as follows: June 5, 1893, $10; Sept. 5, 1893, $50; Jan. 5, 1894, $120.

What was due March 8, 1894?

1012. In the United States courts, and in those of some of the states, interest for a portion of a year is taken by days, upon the basis of 365 days to the year.

To make the work easier for the pupils, however, the year of 360 days should be used in the examples given, and the time between dates should be found by compound subtraction.

PRESENT WORTH AND TRUE DISCOUNT.

1016. Problems are frequently met with in books, in which the "present worth" is asked of a sum of money payable at a future date.

1017. 1. What is the present worth of $150 payable in 1 year 6 months, interest 6% ?

By this is meant what sum at 6% interest will amount to $ 150 in 1 year 6 months? Or,

Given the amount ($150), rate 6%, time 1 yr. 6 mo., to find principal.

x + (x × 180 × 11) = 150.

1018. By "true discount" is meant the difference between the sum payable at a future time and its "present worth."

2. What is the "true discount" of $150, payable in 1 year 6 months, interest 6% ?

The amount $150, rate 6%, time 1 yr. 6 mo., are given. Find the interest.

SURFACES AND VOLUMES.

1024. Slate Problems.

1. If a piece of cloth is 20 yards long and 4 yd. broad, how broad is another piece of cloth 12 yards long that contains as many square yards as the former?

2. An iron beam 16 ft. long, 24 ft. broad, and 8 in. thick, weighs 1,280 lb. What is the length of a similar beam whose breadth is 31 ft., thickness 7 in., and weight 2,028 lb.?

3. What will it cost to carpet a room 224 ft. long by 15 ft. wide with carpet 24 ft. wide, costing $1.50 per yd.?

4. What is the length of a box 63 ft. wide and 71⁄2 ft. high, that will exactly contain 12 boxes 4 ft. long, 3 ft. wide, and 21 ft. deep?

5. What is the value, at $120 per acre, of a square field whose side is 35.25 chains?

6. What is the area in square feet of a triangle whose base is 18 ft. 4 in., and whose altitude is 11 ft. 10 in. ?

7. What is the area of a circle whose diameter is 7.5 feet, the area of the circle being .7854 times the area of the square that will just enclose it?

8. Find the capacity, in bushels, of a bin 22 ft. long, 14 ft. wide, 12 ft. high?

9. How many gallons will a tank hold, its dimensions being 4 ft. 1 in. by 3 ft. 8 in. by 2 ft. 3 in.?

10. How many square yards are there in the walls and the ceiling of a room 21 ft. long, 18 ft. wide, 12 ft. high? Make a diagram.

11. A tank 5 ft. by 6 ft. by 7 ft. can be emptied by two pipes, one of which discharges 9 gallons per minute and the