649. Average Storage. When goods are constantly being received and delivered average storage is more convenient. Storage is paid on the amount of goods actually in storage for any one period. Settlement is made at stated intervals instead of on the withdrawal of goods. Example. May 1 received 140 cases; May 4 received 90 cases; May 10 delivered 100 cases; May 20 delivered 60 cases; May 24 received 300 cases; May 28 delivered 270 cases. Storage ¢ per case per day, payable 1st of each month. Using Average Storage find the charges in each of the following: 1. September 17 received 430 bu.; Sept. 9 received 160 bu.; Sept. 10 received 445 bu.; Sept. 12 received 754 bu.; Sept. 13 delivered 1560 bu.; Sept. 15 received 1860 bu.; Sept. 17 received 2490 bu.; Sept. 18 delivered 1680 bu.; Sept. 24 delivered 1710 bu. Storage 1¢ per 25 bushel per day. Find storage due Oct. 1. 2. July 15 received 1000 bu. wheat; July 20 received 800 bu. ; July 21 delivered 1200 bu.; July 25 received 7500 bu.; July 30 delivered 4000 bu.; Aug. 10 delivered 3000 bu. Storage 1¢ per 20 bushels per day. Find storage Sept. 1. 3. October 20 received 500 bu. of potatoes; Nov. 1 received 1200 bu.; Nov. 10 delivered 1000 bu.; Nov. 15 received 700 bu. Find average storage at 1¢ per 15 bushels per day, Dec. 1. 66 CHAPTER XLVI BUILDING AND LOAN ASSOCIATIONS 650. A Building and Loan Association is a corporation whose purpose is to encourage thrift and saving and to facilitate the owning of houses among its members." There are many thousands of such associations in existence in the United States and other countries. These associations are now regulated more or less closely by law in the various states.* 651. Shares in Building and Loan Associations. — Shares ranging in par value from $25 to $500 (but generally $200) are issued by these associations and sold to subscribers or members on weekly or monthly installments of 25¢ (per week) or $1 per month for each share. Members continue to pay the installments until the sum paid in, together with the accumulated profits, amount to the face value of the shares, at which time they are entitled to withdraw the face value of the shares in cash. 652. Income. The income of the association consists of dues paid each month, of fines, premiums, interest on loans, and profits from withdrawals. 653. Interest on Loans. Members borrowing from the association are obliged to pay interest the same as if they borrow from any other source. 654. Fines. Subject to general restrictions each association adopts its own by-laws. According to these, fines are usually imposed for failure to pay dues promptly. The fine may be a fixed amount for each share, say 10¢ a month per share, or it may be a certain per cent on the unpaid dues. * These institutions had their origin in England in 1795, were first established in the United States in 1831, and have become generally popular in Europe and the United States. 655. Premiums. The method of making loans varies. In some associations the available money is loaned to the members offering the highest rate of interest. (Building and Loan Associations are usually exempt from usury laws when loaning to their own members, since the members share in the profits.) In other cases the rate of interest is fixed, but the loan is made to the member offering the largest cash premium. The premium is deducted from the loan, thus forming a kind of bank discount. In still other cases the loan is made to the member offering to pay interest for the longest time in advance. In all cases there is some kind of competitive bidding for the loans. 656. Book Value of Shares. The books of the association show at any time the amount paid in on each share together with the apportioned profits. This is called the book value of the share. 657. Profits from Withdrawals. - Members frequently find it necessary or desirable to withdraw the cash value of their shares before they mature. In such cases the amount actually paid in plus a certain low rate of interest is allowed. The by-laws usually specify that the withdrawal value shall be less than the true value or book value, the exact rate being fixed from time to time by the directors. The rate of interest actually obtained by investors in building and loan associations is usually rather high. The reason is to be found in the many sources of revenue enumerated above. 658. Kinds of Associations. There are four principal kinds of associations in operation in the United States: (1) Single Series, (2) Several Series, (3) Continuous, (4) The Dayton or Ohio Plan. Of these the Several Series is the most common and is the only one discussed here. 659. Several Series Plan. Suppose an Association is started January 1, 1915. A series of 500 shares is issued. If these are fully subscribed for by April 1, another series, say of 500 shares, is issued and offered for subscription. In this manner new series are issued quarterly, semi-annually, or annually in such amounts as may be required to satisfy the demand. In case there is only one 660. Finding Book Value of Shares. series the profits are apportioned by dividing the total profits by the number of shares. In case there are several series the method usually used is shown in the following: Shares were issued and subscribed for as follows: January 1, 1915, 500 shares; April 1, 600 shares; July 1, 400 shares; October 1, 800 shares. Profits from January 1, 1915, to January 1, 1916, $720. Find the book value of one share of each series January 1, 1916. (To find the investment for one month for one share of each series we notice that the investment for the first month is $1.00, for the second $2.00, for the third $3.00, and so on. Hence in the case of the first series we need to find the sum of the arithmetic series 1+ 2+ 3...+12. This sum is half the number of terms, multiplied by the sum of the first and the last terms. That is, 6 × (1+12) = 78. For the remaining series we have 4 45, 3(1 +6) = 21 and 11⁄2(1+3) 6 respectively.) Solution. = = = Series (1+9) = = 78 Series 4 × 10 = 45 3 X 7 Series 1 X 4 39000 = 27000 Investment for one mo. on a share of 1st Series 6 X 13 = 79200 profits on one dollar for one month .710 profit on share of 1st series .410 profit on share of 2d series .191 profit on share of 3d series .0091 = .055 profit on share of 4th series The difference of $1.40 is due to the omission of decimals. The error is not sufficient to warrant the use of five decimals to correct it. PROBLEMS 1. Shares were issued and subscribed for as follows: January 1, 1914, 200 shares; July 1, 1914, 250 shares; Jan. 1, 1915, 400 shares; July 1, 1915, 300 shares; Jan. 1, 1916, 250 shares; July 1, 1916, 500 shares. Total profits to Jan. 1, 1917, $1470. Find the book value of these shares on this date. 2. Shares were issued and subscribed for as follows: Apr. 1, 1915, 100 shares; July 1, 150 shares; Oct. 1, 300 shares; Jan. 1, 1916, 250 shares; Apr. 1, 1916, 350 shares. Profits to July 1, 1916, $960. Find the book value of these shares on this date. 3. If, in Example 1, above, 10 shares of the first series, 20 of the 2d, 25 of the third, and 2 of the fourth were withdrawn on January 1, 1917, interest being allowed at the rate of 4%, what would be the association's share of the profits on these? Suggestion. To compute the interest find the investment for one month of the payments on the withdrawn shares. Thus on the first series 36 payments had been made. Hence for one share the investment for one month was 36 X (1 + 36) 18 X 37: = 666. = 4. Shares were issued and subscribed for as follows: April 1, 1915, 400; July 1, 350; Oct. 1, 500; Jan. 1, 1916, 250; Apr. 1, 1916, 750. Withdrawn Oct. 1, 1915, 20 shares of the April 1 series, and Apr. 1, 1916, 50 shares of the July 1, 1915, series. Earnings to July 1, 1916, $1950. Find book value of shares on that date, the rate of interest being 4%. Suggestion. On the April shares withdrawn Oct. 1, 6 payments had been made. Hence investment is equal to one dollar for § (6 + 1) = 21 months. Hence the earnings to be divided are 1950 8.90 = $1941.10. The problem is now solved exactly like that on page 463, but we must remember that the number of shares in the first series has been reduced to 380 and of the second series to 300. 5. Series issued and subscribed for as follows: July, 1914, 200; Jan. 1, 1915, 300; July 1, 1915, 500; Jan. 1, 1916, 450; July 1, 1916, 760. Withdrawals, Jan. 1, 1916, 30 shares of 1st series; Mar. 1, 1916, 20 shares of 2d series; July 1, 1916, 30 shares of 1st series; Oct. 1, 1916, 5 shares of 2d series. Earnings to Jan. 1, 1917, $970. Find book value of shares on this date. |