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CASE II. The proceeds of a note, time, and rate, being given,
to find the face.
WRITTEN EXERCISES. 1. I wish to borrow $500 from bank; what must be the face of my note at 30 days, so that when discounted at 6% I shall receive that amount?
Discount on $1 for 33 days = $.0055.
$500 = .9945 = $502.77 face of note. ANALYSIS.—We find the proceeds of $1 for the given rate and
to produce $500 proceeds will require as many dollars as .9945 is contained times in 500, or $502.77.
RULE. Divide the given proceeds by the proceeds of one dollar for the given time and rate; the quotient will be the face of the note.
2. What must be the face of a note at 90 days, that when discounted at 6% the proceeds may be $450?
3. If the proceeds are $1200, the time 60 days, and the rate of discount 6%, what must be the face of the note?
4. Bought a bill of goods amounting to $989.50; for how much must I give my note at 60 days, so that when discounted at 6% it will exactly pay the bill?
5. If I buy a house for $2910, how large a note at 6 months must I have discounted at 6%, in order to pay cash for it?
6. Find the face of a note at 30 days, which when discounted at 7% will yield $450.25.
WRITTEN EXERCISES. 1. If I invest $21000 in a 6% stock, at 105, what will be the amount of my income?
ANALYSIS.—At 105, the cost of each $1 of stock is $1.05. $21000 - 1.05 = $20000 = face of the stock. 6% of $20000= $1200 income.
2. I invest $6480 in city 6's, at 108; what income does the investment yield me?
3. What income will $8000 yield me, if invested in Missouri 6's, at 95?
4. My broker invests $8950 in Maryland 5's, at 89, brokerage 1 %; what income will the investment yield me?
ANALYSIS.—1% of $1=1 cent. $.89+$.002=$.891, the total cost of $1 of stock.
5. I invest $11000 in U. S. 10-40's, selling at 1093, brokerage 1%; what will be my income therefrom?
6. A invests $5600 in a 6% stock, at 112, and B the same amount in a 5% stock, at 80; which investment yields the greater income, and how much?
7. I sell a house which rents for $200 per annum, for $3300, and invest the proceeds in city 6's, at 110; is my income incrcased or diminished thereby, and how much?
8. What income will $5000 yield me if invested in New York 6's, at par?
9. What income will $10000 yield if invested in a 4% stock, at 65?
CASE II. . To find the rate per cent. of income an investment
WRITTEN EXERCISES. 1. If I buy 6 % bonds at 95, what is my rate of income? ANALYSIS.—$1 of stock costs me $.95 and yields me $.06. .06 • .953.0699, or 699%.
2. What is the rate of income upon an investment in U. S. 10-40's, at 114?
3. I buy U. S. 5-20's, at 112; what rate of income do I realize on my investment?
4. What % will my money yield me if invested in city 6's, at 1114, brokerage 4 %?
ANALYSIS. – $1.11 + $.001, brokerage=$1.12, the cost of $1 of stock.
5. I buy a house for $3000, which I rent at $20 per month; the taxes amount to $40 per annum, and the repairs to $20; what % do I get for my money, and how much greater % would the same amount have yielded me if invested in a 6% stock, selling at 90?
6. If a stock paying 8% dividend is selling at 8% premium, what rate % of income will it yield as an investment?
79. If a stock paying 8% dividend is selling at 8% discount, what rate % of income will it yield as an investment?
8. What is my rate of income from a 10% stock, purchased at 124?
9. Bought a stock at 131, which pays 2% per annum; what is my rate of income?
10. What per cent. of income will a 5% stock yield, if purchased at 110?
CASE III. To find what amount must be invested, to yield a
WRITTEN EXERCISES. 1. What sum must be invested in 6% railroad bonds, selling at 90, to obtain an income of $1200?
$1200 = .06 = $20000, face of stock.
$.90 x 20000 = $18000.00, amount invested. ANALYSIS.-As $1 of stock yields $.06 income, to yield $1200 income will require as many dollars of stock as .06 is contained times in $1200= $20000; and as $1 of stock costs $.90, $20000 of stock will cost 20000 times $.90= $18000, the amount invested.
2. If Philadelphia 6's are selling at 1127, what sum must be invested to secure an income of $800 ?
3. I wish to secure an annual income of $1800; what amount must I invest in U. S. 41 % bonds, selling at 108, to yield that income?
4. I have $2000 on interest at 6%; what sum must I invest in 8% school bonds, selling at 98, to yield the same annual income?
5. The U. S. 5-20 bonds of 1882 bear interest at 5%; if they sell at 1093, how much must my broker invest for me to secure an annual income of $1000, brokerage 1 %?
ANALYSIS.—Each $1 of stock will cost me $1.098 +$.001 =$1.10.
6. What sum must I invest in a 7% stock, selling at 102, to pay the interest at 6% on an irredeemable ground rent of $1400?
7. What sum must be invested in a 10% stock, which is worth 140, to secure an annual income of $2500?
CASE IV. To find the price at which a stock must be bought, to yield a given rate of income upon the investment.
WRITTEN EXERCISES. 1. At what price must I buy a 6% stock, that it may yield 7% income on the investment?
ANALYSIS.—The income of $1 of stock is $.06, which is 7 % of the price paid for $1 of the stock. .06–.07=.855: hence the stock must be bought at 85%.
2. What must I pay for New York 6's, to realize 5% income on the investment?
3. At what premium must I buy an 8% stock, to obtain 6% income on my investment?
4. I wish to secure 6% income on a stock which pays 7% ; at what price must I purchase it?
5. At what rate would I have to purchase U. S. 10-40's, in order to secure 6% income on the investment?
6. At what rate must I buy any 6% stock, that it may yield me 6% income on the amount invested?
7. What must I pay for a 6% stock, that it may yield me 10% annual income?
8. What must I pay for a 5% stock, that it may yield 41% income?
GOLD INVESTMENTS. The term Currency is here used to denote the circulating medium employed instead of gold. When this circulating medium depreciates in value, gold is withdrawn from circulation, and becomes an object of investment, and is said to rise or fall as the value of the currency fluctuates.