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06 interest for 1 year. +1.00
1.06 amount for 1 year.
.0636 interest for 2d year. +1.06
1.1236 amount for 2 years.
.067416 interest for 3d year. +1.1236
1.191016 amount for 3 years.
.02382032 interest for 4 months. +1.191016
1.21483632 amount for 3 years and 4 months. It will be sufficiently exact to use the first four decimals $1.2148. This multiplied by 143.17 will give the answer.
59. Make a table which shall contain the amount of 1 dollar, for 1 year, for two years, for 3 years, &c. to 20 years, at 5 per cent. and at 6 per cent. Reserve five decimal places.
N. B. The same table will serve for sterling money, or any other, if the parts are expressed in decimals.
137745-159384 1.551334.6894810 2.529563.02550 3,52.9245.9.2.62 1.6288947908420 2.655973.20713
60. What is the compound interest of $17.25 for 2 years and 7 months, at 5 per cent. ?
Note. From the table take the amount of 1 dollar for two years, at 5 per cent. and compute the interest on it for 7 months, at 5 per cent. as in simple interest; add this to the amount for two years. This will be the amount of 1 dollar for 2 years and 7 months. Multiply this by 17.25; this will be the amount of $17.25 for the time. Then to find the interest, subtract the principal from the amount.
61. What will $73.42 amount to in 4 years, 3 months, and 17 days, at 6 per cent. compound interest?
62. A note was given 13th March, 1815, for $847.25; how much had it amounted to on the 7th November, 1820.. at 6 per cent. compound interest?
63. How much would the sum in the last example have amounted to in the same time at simple interest?
64. What is the compound interest of $1753 for 11 years 10 months, and 22 days, at 6 per cent. ?
65. A note was given 11th May, 1813, for $847, rate 6 per cent. compound interest. The following payments were
made; 18th February, 1815, $158; 19th December, 1816, $87 5th October, 1819, $200. What was due 8th July, 1822?
66. What will 17£. 13s. 6d. amount to in 5 years, 3 months, at 6 per cent. compound interest?
Note. Change the shillings and pence to decimals of a pound, and proceed as in Federal money. Call the unit in the table 1 instead of 1 dollar.
-67. What is the compound interest of $643, for 7 years, 5 months, and 18 days, at 5 per cent.?
68. What is the compound interest of 143£.7s. 4d. for 19 years, 7 months, at five per cent. 2.
69. 0. A farmer mixed -15 bushels of rye, at 64 cents per bushel; 18 bushels of corn, at 55 cents per bushel; and 21 bushels of oats, at 28 cents per bushel. How many bushels were there of the mixture? What was the whole worth? What was it worth per bushel ?
70. A grocer mixed 123 lb. of sugar, that was worth 8 cents per lb.; 87 lb. that was worth 11 cents per lb.; and 15 lb. that was worth 13 cents per lb. What was the mixture worth per lb. ?
71. A grocer mixed 43 gallons of wine, that was worth $1.25 per gal. with 87. gals. that was worth $1.60 per gal. What was the mixture worth per gal.?
72. With a hhd. of rum, worth $.87 per gal. a grocer mixed 10 gals. of water. What was the mixture worth per gal.?
73. How many gals. of rum, at $.60 per gal. will come to as much as 43 gals. will come to, at $.75 per gal.?
74. How much water must be added to a pipe of wine, worth $1.50 per gal. in order to reduce the price to $1.30 per gal. ?
75. A grocer has two kinds of sugar, one at 8 cents per lb.. the other at 13 cents. He wishes to mix them together in such a manner, that the mixture may be worth 11 cents per lb. What will be the proportions of each in the mixtu.e?
Note. The difference of the two kinds is 5 cents. Therefore if a pound of each kind be divided, each into five equal parts, the difference between one part of each will be 1 cent. If lb. be taken from that at 8 cents, and lb. of that at 13 cents be put in its place, the pound will be worth 9 cents. If & lb. be taken from it, and as much of the other be put in
its place, the pound will be worth 11 cents, as required. The pound then will consist of, at 8 cents, If 5 lb. be mixed, there will be 2 lb. cents. The proportions are 2 lb. at 8 13 cents.
and 3, at 13 cents. at 8, and 3 at 13 as often as 3 lb. at
76. A farmer had oats, at 38 cents per bushel, which he wished to, mix with corn, at 75 cents per bushel, so that the mixture might be 50 cents per bushel. What were the proportions of the mixture?
Note. The difference in the price of a bushel is 37 cents. The difference between of a bushel of each is 1 cent. If 12 of a bushel be taken from a bushel of oats, and of a bushel of corn be put in, its place, a bushel will be formed worth 50 cents, and consisting of corn, and 3 oats. The proportions are 12 of oats to 25 of corn.
It is easy to see that the denominator will always be the difference of the prices of the ingredients, und the difference between the mean and the less price will be the numerator for the quantity of the greater, and the difference between the mean and the greater will be the numerator for the quantity of the less value. Take away the denominators, and the numerators will express the proportions.
77. A merchant has spices, some at 9d. per lb. some at Is., some at 2s. and some at 2s. 6d. per lb. How much of each sort must he mix, that he may sell the mixture at 1s. 8d. per lb. ?
Note. Take one kind, the price of which is greater, and one, the price of which is less than the mean, and find the proportions as above. Then take the other two and find their proportions in the same way.
Less 9d. 9d.
Greater 2s. 6d. 30d.
11d. diff. between less and mean.
10d. diff. between great er and mean.
The proportions are 10 of the less to 11 of the greater.
Less 1s. 12d.
Sd. diff. between less
Greater 2s. 24d.
The proportions are 4 of the less to 8 of the greater, which is the same as 1 of the less to 2 of the greater
The answer is 10 lb. at 9d. to 11 lb. at 2s. 6d., and 1 lb. at 1s. to 2 lb. at 2s.
Other proportions might be found by comparing the first, and third, and the second and fourth.
78. A grocer has two sorts of tea, one at 75 cents per lb. and the other at $1.10 per lb. How must he mix them in order to afford the mixture at $1.00 per lb. ?
79. A grocer would mix the following kinds of sugar, viz. at 10 cents, 13 cents, and 16 cents per lb. What quantity of each must he take to make a mixture worth 12 cents per lb. ?
Note. Those at 13 and 16 must both be compared with that at 10 cents separately.
80. A grocer has rum worth $.75 per gal.; how many parts water must he put in, that he may afford to sell the mixture at $.65 per gal. ?
81. It is required to mix several sorts of rum, at 5s. 7d., and 9s. per gal. with water, so that the mixture may be worth 6s. per gal. How much of each sort must the mixture consist of?
82. A farmer had 10 bushels of wheat, worth Ss. per bushel, which he wished to mix with corn, at 3s. per bushel, so that the mixture might be worth 5s. . per bushel. How many bushels of corn must he use?
Note. Find the proportions for a single bushel as before, then find how much corn must be put with 1 bushel of wheat, and then with 10 bushels. The proportions are 2 of wheat to 3 of corn, consequently 1 of wheat to 11⁄2 of corn, and 10 of wheat to 15 of corn.
83. A farmer would mix 20 bushels of rye, at 65 cents per bushel, with barley at 51 cents, and oats at 30 cents per bushel. How much barley and oats must be mixed with rye, that the mixture may be worth 41 cents per bushel '
84. A grocer had 43 gallons of wine worth $1.75 per gal., which he wished to mix with another kind worth $1.40 per gal., so that the mixture might be worth $1.60 per gal. How many gals. of the latter kind must he use ?
85. Three merchants, A, B, and C, freight a ship with wine. A put on board 500 tons, B 340, and C 94'; in &