It is thus seen that an annuity at compound interest forms a geometrical progression in which the annuity is the first term, 1 plus the rate of interest is the ratio, the number of years is the number of terms, and the final value is the sum of the series. Therefore, by ART. 271, The number in parenthesis is the compound interest of $1 for 4 yr. at 5%, which by the table on page 208 is .215506. Hence The sum = $12000 .215506 = $2586.072, Ans. 2. Find the present value of an annuity of $500 for 6 yr. at 5%. $500 (1.056 - 1). By using the table on page 208, (1.056 — 1) = .340096. Hence the We find the present value by dividing by 1.340096, the compound amount of $1 for 6 yr. at 5%. Hence the To find the final value, divide the annuity by the rate, and multiply the quotient by the compound interest for the given time and rate. To find the present value, divide the final value by the compound amount of 1 dollar for the given time and rate. Find the present value— 3. Of an annuity of $800 for 7 yr. at 4%. BUILDING ASSOCIATIONS. 294. Building and Loan Associations, or Co-operative Banks, as they are sometimes called, are corporations which receive small deposits at regular periods of time, and invest them in mortgages among their own members or stockholders. 295. The Members of an association are the persons who either subscribe for shares as an investment or borrow money of the association. The former are called "non-borrowers," and the latter "borrowers." 296. The Shares are usually $200, and are issued periodically in series. When the sum of the regular payments and profits equals the par value of a share, the series is closed. 297. The Dues, or Installments, consist of one dollar a month on each share held by the members. 298. The Premium is the amount bid by a member in excess of simple interest for the purpose of securing the loan. MODES OF LOANING MONEY. 299. There are three modes of loaning money and fixing the interest used by different associations, known as the Installment Plan, the Gross Plan, and the Net Plan. By the Installment Plan the borrower receives the par value of a share, and pays the premium in monthly installments, together with the dues and interest. ILLUSTRATION.-In borrowing $200 the borrower would receive the full amount and pay 6% interest, or $1 a month, together with the dues and monthly premium. By the Gross Plan the borrower receives only the difference between the face value of the loan and the premium bid, but pays interest on the full amount borrowed. ILL.-In borrowing $200 at a premium of 25%, the borrower receives $200 less $50, or $150, and pays 6% interest on $200, or $1 a month, together with the monthly dues. By the Net Plan the premium is deducted as in the gross plan, but the borrower is charged interest only on the amount he receives. ILL.-In borrowing $200 at 25% premium the borrower receives $200 less $50, or $150, and pays 6% interest on this amount-that is, $9 a year, or 75 cts. a month-together with the monthly dues. 300. Fines are penalties imposed for non-payment of dues or interest. By the Building Association Laws of Pennsylvania fines cannot exceed 2% a month on all arrears, and no fine can be imposed on unpaid fines. 301. The Withdrawal Value of a share is found by adding to the amount paid in on the stock, 6% interest on this sum, and such a share of the profits as is determined by the rules of the association. CASE I. 302. To find the cost of any number of shares. 1. What is the cost of 8 shares of stock in a building association which has been running 6 yr. 4 mo., payments $1 per month? 2. What is the actual cost of 20 shares of stock in a building association which has been running 5 yr. 8 mo., payments $1 per month? 3. I own 10 shares in the 1st series, 16 in the 2d, 20 in the 3d of the West End Building and Loan Association; if the 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? 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. 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% ? of $1 for 1 mo. at 6% is ct., and for (66 × 67) mo. is $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? |