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11. At an average price of 55 cts. per bushel, and a charge
of 21% commission, how many bushels of grain can be bought for $4510?
Hint. First find the cost of 1 bu., including commission. 12. A landau was sold for $488, at a gain of 22%.
Required the cost. 13. A milkman's gallon measure was too small by į gi.
What was the rate per cent of fraudulent gain? 14. A merchant paid $112.50 for 75 yds. of silk, of which
15 yds. were worthless. At what price per yard must the remainder be sold to gain 20% on the
purchase-price of the whole ? 15. For selling goods, an agent received $106.83 commis
sion, 24% for selling, 24% for guaranteeing pay
ment. What sum was received for the goods ? 16. A dealer bought 70 bags of wool at $32 a bag; 10%
of it proved unsalable. For what price per bag must he sell the rest to realize 15% on his pur
chase ? 17. A lady paid for investing money $9.374 brokerage,
rate %. Required the amount invested. 18. From a stack of hay, 7 t. 11 cwt. were sold, which was
754% of the whole. What did the stack contain
before the sale ? 19. A carriage worth $250 was bought for $50 less, and
sold for $25 more, than its value. What was the
rate of gain on the price paid ? 20. A man left 30% of his estate to his wife, 50% of the
remainder to his son, 75% of the residue to his daughter, and the balance, $546, to a family servant. Required the value of the estate.
21. What per cent of it is .? of 1 is 19? 22. A man sold 36 horses for $200 each: on half of them
he gained 20%, and on half he lost 10%. What
was his gain per cent on the whole sale ? 23. A gentleman sent to a broker $1281.25 to be invested
in land at $62.50 an acre. A commission of 21% being charged for buying, how many acres were
bought? 24. The dimensions 10, 8, and 6, of a rectangular bin being
increased 10%, what will be the rate per cent of
increase in capacity ? 25. One-half of a stock of goods valued at $612.60 was
sold for of the value of the whole stock. What
was the gain per cent? 26. A roll of 140 yds. of carpet was sold for $72, at a loss
of 10%. What should it have brought per yard to
insure a gain of 15% ? : 27. A railroad company with $9,000,000 capital declares
a dividend of $360,000. What sum will be received
on 120 shares of $ 100 each? 28. Ten per cent of a roll of carpet having been sold to
one man, 10% of the remainder to another, 30.375
yds. are left. How many yards were there at first? 29. At an annual premium of $405, rate 14%, of the
value of a mill is insured. What is the entire value
of the mill ? 30. A broker buying cotton at $% commission retained
$75 for his commission, and paid $25 for storage. What sum was sent by his employers to cover the whole expense of investment ?
31. What sum must be insured upon a library to cover its
entire value, $18,000, and the premium at 14% ? 32. A merchant placed 80% of his year's profits in a bank;
having drawn out 20% of this deposit, $2880
remained. What were his profits for the year? 33. Required the tax-rate, in a city appropriating for pub
lic expenses $147,000, to be assessed on property
worth $35,000,000. 34. A lady bought a house for $7965, which rented for
$841.85. The taxes were $50; repairs, $75. What
rate per cent did the investment yield ? 35. A premium of $960 was paid for full insurance on a
ship and cargo, at 11%. The cost of the cargo was 60% of the cost of the ship. What was the value
of each? 36. Find the entire cost of 4000 bbls. of flour purchased
by an agent, at $7 a barrel, who charged 3% com
mission, and paid $315 for freight. 37. How many barrels of flour can be bought for $5924.38
by an agent' who pays $7 a barrel for the flour, charges 3% commission, and pays $315 for the
freight? 38. The insurance on the value of a hotel and furniture
cost $300. The rate being 75 cts. on $100, what
was the value of the property ? 39. What is the duty, at 25 cts. per gallon, on 48 bbls.
of turpentine, 31 gals. making a barrel, and 5%
being allowed for leakage ? 40. How much must be insured on goods worth $4500, at
5%, so that the value of the goods and the premium may be repaid in case of loss ?
INTEREST AND DISCOUNT.
215. Interest is the payment made for the use of money. . The interest to be paid for the use of a given sum of money differs from the payments considered in the last chapter, in that it depends upon the time for which the sum is loaned as well as on the rate per cent charged.
216. The sum loaned is called the principal. The principal and interest together is called the amount.
SIMPLE INTEREST. 217. If 100 be taken as the representative of the principal, the rate will represent the interest for one year; the product of the rate by the number of years will represent the whole interest.
Thus, if the time be 4 yrs., and the rate per cent 5, the interest will be represented by 20, and the amount by 120. Find the interest on $512 for 2 yrs. 4 mos., at 6%.
21 = 2 yrs. 4 mos.
218. In most business transactions the time for which interest is required is 1, 2, 3, or 4 months (30 dys. being reckoned 1 mo.), and the rate of interest is 6%, that is, % a month.
Hence the interest at 6% on a given sum for 2 mos. (or 60 dys.) is found by moving the decimal-point two places to the left; for 1 mo., 3 mos., 4 mos., by moving the decimal-point two places to the left, and multiplying by 1, 11, and 2 respectively.
Thus, the interest on $ 2500 for 2 mos. is $ 25.00; for 1 mo., $12.50; for 3 mos., $37.50; for 4 mos., $50.
Find the interest on $1120 for 3 yrs. 2 mos. 18 dys., at 6%.
The interest at 6% for 1 yr. = 0.06 of the principal.
3 yrs. = 3 X 0.06 = 0.18
3 yrs. 2 mos. 18 dys. = 0.193 of the principal. And 0.193 of $1120 = $216.16.
219. The six per cent method may be employed for any rate per cent by first finding the interest at 6%, and then taking such a part of the interest as the given rate is of six per cent.
Thus, the interest at 41% = 39 = of the interest at 6%. In this case, we should diminish the interest at 6% by 1 of itself. The interest at 8% is f = 4 of the interest at 6%. In this case, we increase the interest at 6% by } of itself.
220. To compute interest for days at 6%, we move the decimal-point in the principal three places to the left, and multiply by one-sixth of the number of days.