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series are 8, 9, and 10 yr. respectively in maturing, how much has my stock cost me, having been fined twice at 2% a month for non-payment of dues?

CASE II.

303. To find the amount of arrears and fines due.

1. A owns 12 shares in a building association, and fails to make his payments for 6 successive months; what is the amount of arrears due, including fines at 2% a month?

PROCESS. S=(.02 + .12) 3 6 × $1

The fines on 1 share for 6 successive months will be 2 cts. + 4 cts. + 6 cts. + 8 cts. + 10 cts. + 12 cts. It is thus seen to be the sum of an arithmetical progression whose first term is 2 cts., last term 12 cts., and number of terms (.02 + .12) 3 $.42. The dues on 1 share for 6 mo. are $6; hence the arrears and fines on 1 share are $6.42, and on 12 shares the amount will be $77.04.

$77.04, Ans.

=

6; hence S

=

==

=

$.42

6.00

$6.42

12

2. Mr. Good, having 15 shares in a building association which matured in 10 yr. 4 mo., was fined for. 5 successive months for non-payment of dues; how much did he pay into the association, including fines at 2% a month?

3. What is the net profit on 20 shares of stock in a building association which expires in 9 yr. 8 mo., the shares being worth $200 at maturity, and fines 2% a month, the holder having been fined for non-payment of dues for 6 successive months?

4. What is the net profit on 30 shares of stock in a building association which matures in 8 yr. 9 mo., the shares being worth $200 at maturity, if the dues are $1 a month and fines 2% a month, the holder being fined on two occasions for nonpayment of dues, the first time for 5 successive months, and the second time for 8 successive months?

CASE III.

304. To find the present value of shares without the profit.

1. What is the present value of 10 shares of stock in an association which has been running for 5 yr. 6 mo., interest at 6% ?

The time is 66 mo.

$11.055

66.000

The first payment on a share, $1,
is on interest 66 months, the sec-
ond payment 65 months, and so
on;
hence the interest on $1 for
the different periods equals the in-
terest on $1 for a number of months
represented by an arithmetical pro-
gression of which the first term is $1,

$77.055
10

$770.55, Ans.

the last term $66, and the number of terms 66, or (66 × 67). The interest

PROCESS.

5 yr. 6 mo.

=

66 × 67
4

Int.

Amt. paid in

=

=

=

66 mo.

of $1 for 1 mo. at 6% is ct., and for 1⁄2 (66 × 67) mo. is

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$11.055.

The present value of 1 share is $66 plus $11.055, or $77.055, and the value of 10 shares is $770.55.

2. What is the value of 32 shares of stock in the Quaker City Building Association paid up for 8 yr. 7 mo., interest 6% ?

3. A owns 12 shares in an association, first series, and 16 shares in the third series; what is his stock worth if the first series is paid up for 7 yr. 6 mo., interest 5%, and the third series is paid up for 5 yr. 8 mo., interest 5% ?

CASE IV.

305. To find the actual cost of a loan to a borrower.

1. B bought a loan of 20 shares in a new series of an association, gross plan, at $15 per share premium; what will be the actual cost of the loan if the series matures in 8 years?

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8 yr. 6 mo. =
$200 $102
102 × 103
24

PROCESS.

2. A bought a loan of 30 shares, new series, in an association at $75 premium, net plan; if the series matures in 9 yr., what is the actual cost of his loan?

=

3. B bought a loan of 20 shares, new series, in an association on the installment plan at 50 cents a month premium; if the series matures in 9 yr., what is the actual cost of the loan?

4. M bought a loan of 30 shares, new series, in an association at $75 premium, net plan; if the series matures in 8 years, what is the actual cost of his loan?

=

CASE V.

306. To find the rate of interest received by a nonborrower.

The monthly payment on 1 share equals $1 dues and $1 interest, or $2, and on 20 shares the payment is $40.

1. D owns 8 shares in an association, dues $1 a share; if the series matures in 8 yr. 6 mo., what rate of interest does he receive?

102 mo.

The first payment is on interest for 96 mo., the second 95 mo., and so on; hence

$3840, and the loan costs

$98, Profit.

$4.37, Int. 1%.

=

=

The sum of the payments on 1 share for 8 yr. 6 mo. is $102; hence the gain is $200 $102, or $98.

The interest on $1 a month for 102 months at 1% is $4.37. The rate is therefore $98 divided by $4.37, or 22.38+%.

22.38+

$98 $4.373
22.38%, Ans.

2. What is the gain % on the stock of an association which

matures in 10 yr.?

3. What is the gain % on the stock of an association which matures in 12 yr.?

4. By the annual report of the West End Building Association, made at the end of the 7th year, the present value of the first series is $160.40; what was the rate of gain at that time?

5. N owns 10 shares of stock in a building association which 'matures in 8 yr. 8 mo.; what rate of interest does he receive on his investment?

CASE VI.

307. To find the interest paid by a borrower.

1. A buys a loan of 10 shares, 60 cents premium a month, on the installment plan; what rate of interest will he pay if the series matures in 8 yr.?

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2. B buys a loan of $3000 at 55 cts. premium a month on the installment plan; what are his monthly payments, and what average rate will he pay if the series matures in 9 yr. 2 mo.?

3. D buys a loan of 10 shares on the gross plan at $60 premium, new series; what rate of interest does he pay if the series matures in 83 yr.?

4. E buys a loan of 12 shares, net plan, at the beginning of a series, at $50 premium per share; what rate of interest does he pay if the loan matures in 10 years?

5. F buys a loan of 20 shares in an association, at 65 cts. a month premium, at the beginning of the 4th year; what rate of interest does he pay if the series matures in 9 yr.?

THE METRIC SYSTEM

OF WEIGHTS AND MEASURES.

308. THE Metric System of weights and measures originated in France in 1795, and was adopted by the leading countries of Europe and South America, in many of which it was made compulsory. In 1864, Great Britain by act of Parliament permitted its use throughout the empire, and similar action was taken by the United States Congress in 1866. Although the system is very simple, it has not been generally adopted in this country, its use being confined principally to the sciences and to the operations of the Coast Survey depart

ment.

309. The Metric System is based upon the decimal system of notation.

The lower denominations are expressed by writing before the name of the unit

Milli-, to denote one-thousandth of the unit.

Centi-, to denote one-hundredth of the unit.
Deci-, to denote one-tenth of the unit.

The higher denominations are expressed by writing before the names of the unit

Deca-, to denote ten times the unit.

Hecto-, to denote one hundred times the unit.
Kilo-, to denote one thousand times the unit.
Myria-, to denote ten thousand times the unit.

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