Coöperative Banks.

680. A coöperative bank is a mutual corporation with the object of the accumulation of a capital to be loaned to its members, especially for the purchase of homes.

681. Shares. The capital stock is usually divided into shares of final value $200 each, that are paid for in monthly instalments of $1 each. The number of shares that any member may purchase is limited, usually to twenty-five. Each shareholder pays $1 a month per share until his shares are worth $200 each. The shares are then said to be matured. At maturity the shareholder receives $200 in money for each share he holds.

If no profits were added to the value of the shares, it would take 200 months, that is, 16 years 8 months to mature the shares; but the profits generally reduce this time to between 10 and 12 years.

682. Loans. Any shareholder may borrow $200 on each share he holds, provided he furnishes the security required by law. Security may be by mortgage upon real estate or upon the shares themselves. If the shares are offered as security, no shareholder is allowed to borrow more than the present value of his shares.

The amount of a loan is usually limited to $2000.

683. When the accumulation of the various payments has reached a certain sum, these funds are offered at auction and loaned to the shareholder who offers proper security and bids the highest premium, in addition to interest at the rate of 6% per annum. This interest and premium is added to the general fund, and at stated times is credited equally among the various shares.

684. Fines. To prevent payments falling into arrears, a fine, usually 2 cents a month on every dollar not paid

when due, is imposed on delinquent shareholders, whether the delinquency is the monthly instalment, interest, or premium.

685. Examples. 1. Find the cost at compound interest of a coöperative bank share, if the share matured in 11 years, and money was worth 4%.

=

SOLUTION. 11 yr. 132 mo.

The rate of interest was 4% yearly, or 3% monthly.

$1 was paid monthly for 132 mo.

By the four-place table of logarithms, the value of this fraction is found to be $163.80; by a seven-place table, the value is $165.46. The seven-place table gives a very close approximation.

2. Find the cost at compound interest of a loan of $200 from a coöperative bank, if the borrower pays $1 per month interest. The shares are worth $60, and mature in 7 years, and money is worth 4%.

SOLUTION. The borrower pays monthly $2 for 7 yr., that is, 84 mo. The final value of $2 deposited monthly for 84 mo. at 4% is found by § 673 to be $191.40, and the compound amount of $60 at 4% for 7 yr. is $78.96. Hence, the cost of the loan is $191.40 + $78.96 = $270.36.

EXERCISE 161.

Find the cost at compound interest of a

1. Coöperative bank share that matured in 10 years, when money was worth 44%.

2. Coöperative bank share that matured in 11 years, when money was worth 5%.

3. How much more does it cost to borrow $2000 from a coöperative bank, monthly interest being $12, and the shares maturing in 10 years, than to borrow $2000 at compound interest for 10 years, if money is worth 5% in both cases?

CHAPTER XXI.

MISCELLANEOUS PROBLEMS.

In solving these problems, logarithms should be used whenever they can be used with advantage.

1. Make six different numbers with the digits 1, 2, 3, and find their sum.

2. Make six different numbers with the digits 2, 3, 5, and find, by logarithms, their continued product.

3. Make six different numbers with the digits 8, 7, 3, and find, by logarithms, their continued product.

4. Find, by logarithms, the missing term in each of the following proportions:

(i) 7.13:3.57:: 4.18: ?. (ii) 5.89:76.3::?:38.7.

(iii) 7.37?:86.1:43.7.

(iv) ?:69.73.79:29.4.

5. Find, by logarithms, the value of 0.08; 27343; 21.97; 78.6; 9.71; 7.936*.

54.792 X 3.1416 x 12.72

6. Find the value of V

0.5236 × 14.28

7. If the air-line distance between two points is 1534 ft., and the difference of level is 34 ft., what is the horizontal distance between the two points?

8. If the road distance is 1 mi., and the rise 347 ft., find the horizontal distance.

9. If the road distance is half a mile, and the horizontal distance 2513 ft., find the difference of level.

10. The diagonal of a rectangular floor is 34.6 ft., and the width is 17.8 ft. Find the length of the floor.

11. The height of a tower on the bank of a river is 55 ft., and the length of a line from the top of the tower to the opposite bank is 78 ft. Find the breadth of the river.

12. The number of seamen at Portsmouth is 800, at Charlestown 404, and at Brooklyn 756. A ship is commissioned whose complement is 490 seamen. Determine the number to be drafted from each place to obtain a proportionate number from each.

13. Show, without division, that 36,432 contains 8, 9, 11 as factors.

14. Find the smallest multiplier that will make 47,250 a perfect cube.

15. Find the proper fraction that, when reduced to a continued fraction, has for quotients 1, 3, 5, 7, 2, 4.

16. If the meter is equal to 1.09362 yd., find a series of four fractions that will express more and more nearly the true ratio of the meter to the yard.

17. Find the square factors contained in 33,075.

18. The height of St. Peter's, Rome, is fo of a mile, and that of St. Paul's, London, is of a mile. How many feet higher is St. Peter's than St. Paul's?

19. How many days elapsed between the annular eclipse of May 15, 1836, and that of March 15, 1858?

20. In a gale, a flagstaff 60 ft. high snaps 28.8 ft. from the bottom; and, not being wholly broken off, the top touches the ground. If the ground is level, how far is the top from the bottom?

21. Seventeen trees are standing in a straight line, 20 yd. apart; a man walks from the first to the second and back, then to the third and back, and so on. How far does he walk?

22. A canal is 14 mi. long and 48 ft. wide. At one end is a lock 80 ft. by 24 ft., with a fall of 8 ft. 6 in. How many barges can pass through the lock before the water in the canal is lowered 1 in.?

23. Find the capacity, in liters and in bushels, of a box 1.7m long, 87cm wide, and 31cm deep.

24. Find the number of kilograms of olive oil, specific gravity 0.915, required to fill a rectangular vessel 2.3m long, 1.8m wide, and 74cm deep.

25. How many tons in a block of marble 4 ft. long, 34 in. wide, 17.3 in. thick, specific gravity 2.73 ?

26. Find the surface of a sphere 18.3 in. in diameter. 27. Find the number of acres in a circular field 213 yd. 2 ft. in diameter.

28. How many cubic inches in a 10-inch globe? in a 20inch globe? What is the ratio of their volumes?

29. How many balls 3 in. in diameter can be cast from a pig of iron 7 ft. long, 6.7 in. wide, 3.8 in. thick, if the waste in melting and casting is reckoned at 34% ?

30. Find the difference in length, at 80° F., of a glass rod and a steel rod, each 3 ft. long at 0° C., if the expansion at 100° C. is 0.00085 for glass and 0.0012 for steel.

31. A grain of gold is beaten into leaf to cover 56 sq. in. What weight will be required to gild the faces of a cube whose edge is 3 ft.?

32. What premium must be paid, at the rate of 43%, for insuring a vessel worth $100,000, in order that in the event of loss the owner may receive both the value of the ship and the premium?

33. By selling goods at 60 cents a pound, 8% is lost. What advance must be made in the price to gain 15% ?

34. The sharpest grade on Mt. Washington Ry. is 1980 ft. to the mile. What fraction of a foot is the rise for each foot? What is the per cent of grade?

35. Find the square root, to four decimal places, of the reciprocal of 0.0043.

36. The population of a city in 1890 was 12,298, showing a decrease of 83% on its population in 1880; in 1880 there was an increase of 71% on the census of 1870. What was its population in 1870 ?