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265. To find what income any investment will produce.
1. What income will be obtained by investing $6840 in stock bearing 6%, and purchased at 95?
SOLUTION. We divide the investment, $6840, by the cost of $1, and obtain $7200, the stock which the investment will purchase (264). And since the stock bears 6% interest, $7200 ×.06=$432, the annual income obtained by the investment.
RULE. Find how much stock the investment will purchase, and then compute the income at the given rate upon the par value.
2. If I invest $867 in 6% bonds at 102, what income will I receive on my investment? Ans. $51. 3. What will be my yearly income, if I invest $8428 in 5 per cents, at 98? Ans. $430.
4. How much stock at a premium of 43% can be bought for $10500, brokerage 1% ? Ans. $10000. 5. If a man invests $4795 in Maryland 5's at 87, brokerage %, what will be his yearly income?
6. Having $10476 to invest, I find I can purchase N. Y. 6's at 107, and Erie R.R. 5's at 961, brokerage %, in each instance. How much more will I receive yearly by investing in the former than in the latter?
7. A having a farm of 109 acres, which rents for $681.25, sells the same for $125 per acre, and invests the proceeds in Pacific R.R. 6's at 1083, brokerage % for purchasing. Will his yearly income be increased or diminished, and how much? Ans. Increased $68.75.
266. To find what sum must be invested to
obtain a given income.
1. What sum must be invested in Virginia 5% bonds, purchasable at 80, to obtain an income of $ 600 ?
$12000, stock required.
SOLUTION. Since $1 of the stock will obtain $.05 income, to obtain $600 will require a par value of $600.05 $12000. Multiplying the par value of the stock by the market price of $1, we have $12000 × .80 $9600, the cost of the required stock, or the sum to be invested.
RULE. I. Divide the given income by the per cent which the stock pays; the quotient will be the par value of the stock required.
II. Multiply the par value of the stock by the market value of one dollar of the stock; the product will be the required investment.
2. If N. Y. 6's are 5% below par, what sum must be invested in this stock to obtain an income of $840?
Ans. $13300. 3. What sum must be invested in 5 per cents at 981, brokerage 1% for buying, to secure an annual income of $1860 ? Ans. $36642.
4. When 5 per cents are quoted at 1081, what sum must I invest to secure an annual income of $1080, brokerage %? Ans. $23436.
5. If I sell $25000 in railroad bonds at 934, and invest a sufficient amount of the proceeds in Pacific R.R. 6's, at 1091, to yield an annual income of $960, and buy a house with the remainder, how much will the house cost me ? Ans. $5957.50.
267. To find what per cent the income is of the investment, when stock is purchased at a given price.
1. What per cent of my investment will I secure by purchasing N. Y. 7's at 105?
.07 ÷ 1.0563%.
RULE. -Divide the annual rate of income which the stock bears by the price of the stock; the quotient will be the rate upon the investment.
2. What is the rate of income upon money invested in 6% bonds, purchased at 87 ? Ans. 628%.
3. What per cent on his money will a man receive annually if he invests in N. Y. 6's at 105 ? Ans. 54%. 4. What is the rate of income upon money invested in Missouri 6's at 75? Ans. 8%.
5. I purchased Pacific R.R. 6's at 1073, brokerage 4%. What is the income on the investment? Ans. 55%.
6. Which is the better investment, Mass. 5's at 981, or Pacific R.R. 6's at 1083, brokerage % in each?
7. If stock paying 10% dividends is quoted at 112, what per cent of income will be realized on an investment in it? Ans. 88%.
8. Which will yield the better income, 8% bonds at 110, or 5's at 75? Ans. 8% bonds at 110, 38% better. 9. Which is the more profitable, and how much, to buy 7's at 105, or 6% bonds at 84?
Ans. 6% bonds at 84, 10% better.
10. What per cent of income does stock paying 10% dividends yield, if bought at 106? Ans. 93%.
11. What per cent will stock which pays 5% dividends yield, if bought at 85? Ans. 51%.
268. To find the price at which stock must be purchased to obtain a given rate upon the investment.
1. At what price must 6% stocks be purchased in order to obtain 8% income on the investment?
SOLUTION. Since $6, the income of one share of the stock, must be 8% of the sum paid for it, we have $6.08 = $75, the purchase price of one share of the stock, usually expressed simply as 75.
RULE. · Divide the annual income which the stock bears by the rate required on the investment; the quotient will be the price of the stock.
2. What must I pay for Missouri 6's that my investment may yield 9% annually? Ans. 66%
3. What must I pay for a 6% stock so that the investment will yield 5%? Ans. 120. 4. What must I pay for 5 per cents, that my investment may yield 8%? Ans. 62.
5. At what price must Vermont 6% bonds be purchased that the person investing may secure 61% upon his money? Ans. 96.
6. At what price must I buy stock that pays 10% dividends, so as to realize 71% on the investment?
7. At what price must I buy 7% stock so as to realize 6% on my investment ? Ans. 1163.
8. At what price must stock, of the par value of $50 a share, and that pays 6% dividends, be bought, to yield an income of 71%? Ans. 40.
9. At what price must 4% stock be bought to pay as good an income as 8% stock bought at par? Ans. 50.
269. A Discount is a deduction from the face of bills, the list price of goods, or from the amount of debt, without regard to time, and is usually expressed by the term "per cent off."
Thus, a discount of 25% means a deduction of 25% from the asking price. A discount of 30% and 10% does not mean 40% off, but that 30% is first to be deducted, leaving 70% of the price, then 10% of 70% of the price, equal to 7%, is deducted from the remainder, leaving 63%; so that the total discount is but 37%. 3 tens and 5% off means three successive discounts of 10% and 5% from the remainder, etc.
In some kinds of business fixed price lists are printed, and when a rise or fall in prices occurs the rate of discount is changed.
270. The List Price is called the fixed price, and the discount is called Trade Discount.
271. The Net Price is the list price, less the discount, or the price received for the goods.
1. What is the net cost of a bill of goods amounting to $975, bought on 4 mo., at 10% discount, and 5% off for cash? Ans. $833.624. Find the net cost and discount of the following bills:
2. Bought for $750, on 3 mo., at 20% discount, and 4% off for cash. Ans. $576; $174.
3. Bought for $365.75, on 4 mo., at 20%, 10%, and 5% off for cash. Ans. $250.17; $115.58. 4. Bought for $260, on 90 da., at 2 tens and 3% off for cash. Ans. $204.28; $55.72. 5. What is the difference on a bill of $650, between a discount of 30%, and a discount of 25% and 5% off?