SOLUTION. The loan was 10 X($200-$95)= $1050; the interest on $1050 for 1 mo. is $5.25; and $10 dues+$5.25 OPERATION. 10× ($200-$95) = $1050, Amt. of loan. $15.25X 24 x.06 $385.06, Interest, 6%. $1525+$385.061 $1910.061, Entire payment. 100 mo. equal lent to the interest on $15.25 for 101 × 100 $1525. Now, the interest on the monthly payments (Case III.) is equiva years at 6%, or $385.061; hence the actual cost of the loan is $1525+$385.061, or $1910.061; therefore $1910.06-$1050, or $860.061, is the interest on the loan for 8 years; and the interest for 1 yr. is $860.06÷8} = $103.2075; hence the rate is $103.2075-$1050 .0983-, or 91%. = 83 Rule.-I. Find the sum of the installments, and the interest on the installments for the equated time at 6%; their sum will be the entire cost of the loan. II. Subtract the amount of the loan from its entire cost; the remainder will be the interest on the loan for the period, from which the rate is readily found by the method of simple interest. 2. Mr. Roscoe buys a loan on 10 shares, new series, of Quaker City Building Association, at $75 premium, Gross plan; what equated rate of interest did he pay for his loan, if the series expired in 8 years? Ans. 12.86%-. 3. Mr. Collins bought of the Provident Building Association a loan on 20 shares, 3d series, at 70 a month premium, at the beginning of the 4th year; if it ran out in 8 years, what equated rate of interest did he pay? Ans. 4.84% +. 4. I buy two loans of 15 shares each in 1st and 5th series, at the beginning of the 5th series, at $9 and “stated premium," Gross plan; what rates of interest shall I pay if both series run out in 9 years? Ans. 616%+; 11,10%%+. 5. I bought loans at $63 premium on 17 shares 1st series, worth $80, and 12 shares 3d series, worth $41.70, Net plan, at the beginning of the 5th year of the association; what equated rates of interest do I pay if the first series runs out in 8 years and the 3d in 9 years? Ans. 2.17%; 5.74%. CASE VI. 945. To find the true profit earned and allowed on withdrawals, less the withdrawal discount. 1. I withdraw at the end of 36 months 28 shares of El Paso Building Association, worth $54.50; what is the true profit earned and what the withdrawal value, the withdrawal discount being 10% ? $1 for X (36+1) × 36, months, which equals 37 X 36 1, = = $3.33, interest; $18.50 profit, minus $3.33 interest, equals $15.17; 54.50 of $15.17 equals $4.13; $3.33+$4.13=$7.46, the true profit; $7.46, less 10%, withdrawal discount, equals $6.71, the withdrawal profit; $36+ $6.71=$42.71, withdrawal value of 1 share, which multiplied by 28 gives $1195.88, the withdrawal value. Rule.-I. Multiply the number of months by the number of months increased by 1 and divide by 4, for 6% interest on the payments, and deduct this from the gross profits. II. Multiply the remaining profits by the present value of a share divided by 200, for profits from premiums, and add this to the interest for the True Profit. Subtract the withdrawal discount from the true profit for the withdrawal profit; and add the payments, for the withdrawal value of a share. NOTES.-1. To find the amount due the association by a borrowing member on withdrawing, add the true premium to the withdrawal value of a share, and subtract the result, less all arrearages, from the par value. 2. Some associations, on a basis of 10 years, allow of the apparent or gross profit for each expired year; others 5 per cent. for every $10 of apparent value, or a percentage of the profit, or a rate of interest on the dues, or a withdrawal value fixed yearly. 3. In the Installment Plan, these rules are not needed, since the present value and true value of profits and shares are alike, and we merely subtract the withdrawal discount from the true profit, and add the payments. 2. At the end of the fifth year of a series estimated at $110.70 full value, I withdraw 20 shares, withdrawal discount 10%; what sum do I realize? Ans. $1778.64. 3. Mr. Wrigley subscribed for 10 shares Quaker City B. A., fifth series, issued July, 1872. If he withdrew from the Association in May, 1879, what would be the withdrawal value of his stock, discount 10%, if the value given in the Report of 1878 should be $135.80? Ans. $1290.09. 4. Mr. Smith returns a loan made on 5 shares, new series, at $58 premium, and withdraws his shares at the end of the third year, withdrawal discount 10%; if a share is worth $56.20, what part of the loan will he return to the Association? Ans. $575.23. 5. The Mutual Loan Association sells a loan at 28% premium on 20 shares new series; after 3 years and 4 months, the loan was paid and the shares withdrawn, withdrawal discount 10%; what balance of loan was due by the rule, if the shares were given at $59 in the last Report? and what by Pennsylvania law? Ans. $2251.84; $2319.04. CASE VII. 946. To find the present value of a share at the close of any period. OPERATION. 1. A Building Association having a first series of 1490 shares, worth at the end of the 1st year $13.448, issues at the beginning of the 2d year a second series of 1600 shares; the receipts of the year on both series are, besides dues, $3950 in premiums, $1225 in interest, $40.25 in fines, and $375 contingent fund for current expenses; what is the value of the shares of each series at the end of the second year? SOLUTION.--The amount of the dues (1490+1600) $12 $37,080, Total Dues. for the 2d year on $3950+$1225+$40.25=$5215.25, Gross Profits. both series is 3090 $13.448X.06 $0.80688, Int. on 1 sh. 1st Series. X$12 $37,080; $0.80688×1490 $1202.2512, Int. on 1st Series. the gross profits $5215.25-$1202.25-$4013, Net Profits. equal the sum of $37,080+$1202.25 $38,282.25, Active Capital. the premiums, in- $4013÷$38,282.25 10.48%, Rate of Profit. terest, and fines, ($12+$0.806) X 10.48 %=$1.342, Profit on 1 sh. 1st. which is $5215.25; $12x10.48% $1.2576, Profit on 1 sh. 2d Series. the interest on 1 $13.448+$0.806+$12+$1.342=$27.596, Ans. share of 1st series $12+$1.257=$13.257, Ans. for the 2d year is = $.80688, and on 1490 shares is $1202.25; and the net profits equal gross profits, $5215.25, minus interest, $1202.25, or $4013, which is to be divided among the different items of capital contributed during the year, called the active capital, consisting of the interest on the previous year's capital and the dues for the year; the interest and dues equal $38,282.25; dividing the net profits by this sum, we have 10.48%, the rate of profit; the profit on 1 share of 1st series equals the sum of interest and dues multiplied by the rate, or $12.806×10.48% $1.342; the profit on 1 share of 2d series equals the dues multiplied by the rate, or $12× 10.48% = $1.257; then $13.448+$0.806+$12+$1.342=$27.596, is the value of a share of 1st series at the end of the 2d year, and $12+$1.257 $13.257, is the value of a share of the 2d series at the end of the 2d year. = Rule.-I. Find the legal interest for the term on the values of the old series at the beginning of the term, and deduct this from the profits of the term, for the net profit. II. Divide the net profit by the sum of the dues for the term and the interest on the previous series, to find the rate per cent. of profit. III. Multiply the sum of the interest and dues for the term on 1 share of each series by the rate per cent. of profit, to find the profit on 1 share. IV. Add the previous value of each share, the legal interest on this value, the dues for the term, and the profit on the share, to find the present value of any share of each series. NOTE.-The contingent fund does not enter into the calculation, as it is usually assessed separately for current expenses. 2. At the beginning of the second year of a Building Association, it has a 1st series of 1350 shares, worth $14.32 a share, and issues a new series of 1500 shares; its receipts for the year on both series are, besides the dues, $3750 in premiums, $1675 in interest, $52.25 in fines, and $350 contingent fund; what is the value of a share of each series at the end of the 2d year? Ans. $28.748; $13.464. 3. At the beginning of the 3d year of the same association a new series of 1250 shares is issued; the receipts for the year are, besides dues, $5175 in premiums, $1650 in interest, $49.75 in fines, and $525.50 for contingent fund; what is the value of a share of each series at the end of the 3d year? Ans. $43.345; $27.086; $12.763. SECTION XIII. PROPERTIES OF NUMBERS. 947. The Properties of Numbers are the truths or principles which relate to them. 948. The Classification of Numbers is based upon their different peculiarities or properties. 949. All Numbers are either Integral or Fractional. This division is made with reference to their relation to the Unit. 950. All Numbers are either Abstract or Concrete. This division is made with reference to their application. 951. All Numbers are either Prime or Composite. This division is made with respect to their composition. 952. All Numbers are either Even or Odd. This division is made with respect to their being or not being a multiple of 2. 953. All Numbers are either Perfect or Imperfect. This division is based upon their relation to the sum of their divisors. 954. The Properties of Numbers, as given in this work, embrace the following subjects: 1. Composite Numbers. 2. Prime Numbers. 3. Even and Odd Numbers. 4. Perfect and Imperfect Numbers. 7. Properties of the Number 7. GENERAL PRINCIPLES. 1. A divisor of two numbers is a divisor of their sum and also of their difference (Prin. 4, Art. 175). |