SOLUTION.

Principal, dated April 12, 1878.....

$650.00

Interest to first payment, May 1, 1879 (1 yr. 19 da.).

41.06

Interest to May 1, '80, or 1 yr. (2d payment being short of 1 yr.)..

34.49

Amount, May 1, '80..

609.35

Amount of second payment to May 1, '80 (2 mo. 20 da.).

62.32

Remainder, or New Principal, May 1, '80...

547.03

Amount, May 1, '81 (1 yr.)......

579.86

Third payment (being less than interest due) draws no interest...

12.10

Remainder, or New Principal, May 1, '81.

567.76

Amount, Oct. 21, '81 (5 mo. 20 da.)..

583.85

Amount of last payment to settlement (4 mo. 1 da.)..

112.22

Balance due Oct. 21, '81......

$471.63

NOTE. For additional exercises in the Connecticut Rule, the student is referred to Art. 554.

907. Vermont Rule for Partial Payments on Notes bearing Annual Interest.

I. When payments are made on notes bearing interest, such payments shall be applied,

66

First, to liquidate the interest that has accrued at the time of such payments; and secondly, to the extinguishment of the principal."

II. When notes are made "with interest annually,"

The annual interests which remain unpaid shall be subject to simple interest from the time they become due to the time of settlement.

III. If payments have been made in any year, reckoning from the time such annual interest began to accrue, the amount of such payments at the end of such year, with interest thereon from the time of payment, shall be applied:

"First, to liquidate the simple interest that has accrued from the unpaid annual interests.

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Secondly, To liquidate the annual interests that have become due.

"Thirdly, To the extinguishment of the principal.

$1500.

BURLINGTON, Feb. 1, 1877.

1. On demand, I promise to pay to the order of Jared Sparks, fifteen hundred dollars, with interest annually at 6%, value received. AUGUSTUS WARREN.

Indorsements:-Aug. 1, 1877, received $160; Nov. 1, 1880, $250. Required the amount due Feb. 1, 1881.

1425.20

256.53

$10.26

5.13

15.39

1697.12

$250.00

3.75 253.75

$1443.37

Remainder, or New Principal...
Annual interest on same from Feb. 1, '78, to Feb. 1, '81 (3 yr.)...

Interest on first annual interest from Feb. 1, '79 (2 yr.)..
Interest on second annual int. from Feb. 1, '80 (1 yr.)....

Amount...

Second payment, Nov. 1, '80..

Interest on same to Feb. 1, '81 (3 mo.).

Balance due Feb. 1, '81.

908. New Hampshire Rule for Partial Payments.

I. When on notes drawing annual interest,

Find the interest upon the principal from date of note to the end of the year next after the first payment, also upon each annual interest to the same date.

II. If the first payt. be larger than the sum of interests due,

Find the int. on such payt. from the time it was made to end of the year, and deduct the sum of payt. and int. from the amount of principal and interests.

III. If less than the annual interests accruing,

Deduct the payment without interest from the sum of annual and simple interest, and upon the balance of such interest cast the simple interest to the time of the next payment.

IV. If less than the simple interest due,

Deduct it from the simple interest, and add the balance without interest to the other interests due when the next payment is made.

Proceed thus to the end of the year after the last payment, being careful to carry forward all interest unpaid at the end of each year.*

1. A agrees to pay B $2000 in 6 yr. from Jan. 1, 1870, with interest annually. On July 1, 1872, a payment of $500 was made; and Oct. 1, 1873, $50. What was due Jan. 1, 1876?

Interest on same for fourth year...

Second payt. (less than the int. accruing during the year).

Balance of fourth year's interest unpaid....

Annual interest on balance of principal for fifth year..

"sixth "

Simple int. on unpaid bal. of fourth year's int. for 2 yr.

Simple interest on fifth year's interest for one year

Balance of principal. . . .

Amount due January 1, 1876.

111.99 + 50.00

$61.99+

111.99+

111.99+

7.43+

6.71 +

1866.60

$2166.71

* Abstract of N. H. Court Rule, Report of Hon. C. A. Downs, State

Superintendent.

909. The Twelve Per Cent Method of Computing Interest.

1. Find the int. of $275.20, for 3 yr. 4 mo. 10 da., at 12%.

SOLUTION.

Int. of $275.20, 1 yr. at 1% = $275.20 x .01 = $2.752.

1 yr. at 12% = $2.752 × 12 =

$33.024.

1 mo. at 12% = 12 mo. at 1% = $2.752. (Art. 578.)

RULE.-For 1 year: Find the interest on the principal at 1%, by moving the decimal point two places to the left, and multiplying the result by 12.

For 2 or more years: Multiply the interest for 1 year by the number of years.

For months and days: Proceed as in Art. 537.

AVERAGE OF MIXTURES.

910. To find the Average Value of a Mixture, when the Quantity and Price of each Article are given.

1. A man mixed 45 bu. oats worth 25 cts. a bushel with 38 bu. corn at 50 cts., and 56 bu. rye at 60 cts. ; what was the mixture worth a bushel?

SOLUTION.-The whole number of bushels mixed is 45+38+56=139. The whole cost of the mixture is $11.25 + $19.00 + $33.60 $63.85.

Now, $63.85÷139 = $0.46 nearly, the price of 1 bushel of the mixture. Hence, the

OPERATION.

$0.25 × 45 = $11.25

0.50 × 38 =
0.60 × 56 =

19.00

33.60

139) $63.85

Ans. $0.46.

RULE.-Divide the value of the whole mixture by the sum of the articles mixed.

NOTES.-1. If an article costs nothing, as water, its value is 0; but the quantity used must be added to the other articles.

2. The process of finding the average value of mixtures is often called Alligation.

2. A grocer had three kinds of sugar, worth 6, 8, and 12 cents per pound; he mixed 112 lb. of the first, 150 lb. of the second, and 175 of the third together. What was the mixture worth per pound?

911. To find the Proportional Parts of a Mixture, the Mean Price and the Price of each Article being given.

3. A grocer desired to mix 4 kinds of tea, worth 5s., 8s., 11s., and 12s. a pound, so that the mixture should be worth 9s. a pound; in what proportion must they be taken ?

9s.

OPERATION.

Col. 1.

2. 3.

5s. 1

8s.

1

11s.

12s.

ANALYSIS.-First find how much it takes of each article to gain or lose a unit of the mean price. Since the mean price is 9s. a pound, 1 lb. at 5s. gains 4s. ; hence, to gain 1s. takes lb., which we place in Col. 1. Again, 1 lb. at 12s. loses 3s.; hence, to lose 1s. takes lb., which we place also in Col. 1, opposite the price compared. In like manner, 1 lb. at 8s. is required to gain 1s., while 1 lb. at 11s. loses 2s.; hence, to lose 1s. takes .lb. We place these results in Col. 2, opposite their prices. Reducing the fractions in Col. 1 and 2 to a common denominator separately, the numerators are the proportional parts required. Hence, the

RULE.-I. Write the prices of the articles in a column in their order, with the mean price on the left.

II. Take them in pairs, one less and the other greater than the mean price, find how much is required of each article to GAIN or LOSE a unit of the mean price, and set the results in Col. 1, opposite to its price. Compare the other couplet in like manner, setting the results in Col. 2.

III. Finally, reduce the numbers in each column separately to a common denominator; the numerators will be the proportional parts required.

NOTES.-1. If there are three articles, compare the price of the one which is greater or less than the mean price with each of the others, and take the sum of the two numbers opposite this price.