NOTE 1. If the interest is to be paid semi-annually, quarterly, monthly, or daily, it must be computed for the half-year, quarter-year, month, or day, and added to the principal, and then the interest computed on this, and on each succeeding amount thus obtained, up to the time of settlement.

NOTE 2. When partial payments have been made on notes at compound interest, the rule is like that adopted in Art. 199.

EXAMPLES FOR PRACTICE.

2. What is the compound interest of $761.75 for 4 years?

Ans. $199.941.

3. What is the amount of $ 67.25 for 3 years, at compound interest? Ans. $80.095. 4. What is the amount of $78.69 for 5 years, at 7 per cent.? Ans. $110.364.

5. What is the amount of $128 for 3 years, 5 months, and 18 days, at compound interest? Ans. $156.717. 6. What is the compound interest of $76.18 for 2 years, 8 months, 9 days? Ans. $12.967.

209. Method of computing compound interest, by means of a

TABLE

SHOWING THE AMOUNT OF $1, OR £ 1, FOR ANY NUMBER OF YEARS, FROM 1 TO 20, AT 3, 4, 5, 6, AND 7 PER CENT., COMPOUND INTEREST.

1.169858

1.423311 1.551328

1.125508 1.215506 1.159274 1.216652 1.276281 1.338225 1.402552 1.194052 1.265319 1.340095 1.418519 1.500730 1.229873 1.315931 1.407100 1.266770 1.368569 1.477455 1.304773 10 1.343916 1.480244

1.262476

1.310796

1.503630

1.605781

1.593848

1.718186

12345678

1.689478

1.838459

9

1.628894

1.790847

209. If the interest is to be paid semi-annually, quarterly, &c., how is it computed? How, when partial payments have been made?

Ex. 1. What is the interest of $240 for 6 years, 4 months,

and 6 days, at 6 per cent.?

Ans. $107.593.

We multiply the principal by the amount of $1 for 6 years in the table, and obtain the amount for 6 years. We then find the interest on this amount for the 4 months and 6 days, and add it to its principal, and from the sum subtract the principal for the answer. Hence,

Multiply the amount of $1 for the given rate and time, as found in the table, by the principal, and the product will be the amount. Subtract the principal from the amount, and the remainder will be the compound interest. If there are months and days in the time, cast the interest for the months and days as in the foregoing rule.

EXAMPLES FOR PRACTICE.

2. What is the interest of $884 for 7 years, at 4 per cent.?

Ans. $279.283.

3. What is the interest of $721 for 9 years, at 5

per cent.? Ans. $397.507.

4. What is the amount of $960 for 12 years, 6 months, at 8 per cent.? Ans. $1389.26. 5. What is the amount of $25.50 for 20 years, 2 months, and 12 days, at 7 per cent.? Ans. $100.058.

6. What is the amount of $12 for 6 months, the interest to be added each month? Ans. $12.364+.

7. What is the amount of $100 for 6 days, the interest to be added daily? Ans. $100.10004.

DISCOUNT.

210. Discount is an allowance or deduction for the payment of a debt before it is due.

The Present Worth of any sum is the principal, which, being put at interest, will amount to the given sum in the time for which the discount is made. Thus, $100 is the present worth of $106, due one year hence at 6 per cent.; for $100 at 6 per cent. will amount to $106 in this time; and $6 is the discount.

NOTE.- Business men, however, often deduct five per cent., or more, from the face of a bill due in six months, or a percentage greater than the legal rate of interest.

211. The interest of any sum cannot properly be taken for the discount; for the interest for one year is the fractional part of the sum at interest, denoted by the rate per cent. for the numerator, and 100 for the denominator; and the discount for one year is the fractional part of the sum on which discount is to be made, denoted by the rate per cent. for the numerator, and 100 plus the rate per cent. for the denominator. Thus, if the rate per cent. of interest is 6, the interest for one year is Too of the sum at interest; but if the rate per cent. of discount is 6, the discount for one year is 18 of the sum on which discount is made.

212. In discount, the rate per cent., time, and the sum on which the discount is made, are given to find the present worth.

These terms correspond precisely to Problem VI. in interest, in which the rate per cent., time, and amount are given to find the principal. (Art. 203.)

213. To find the present worth and the discount of any sum due at a future time.

Ex. 1. What is the present worth of $25.44, due one year hence, discounting at 6 per cent.? What is the discount?

Ans. $24 present worth; $1.44 discount.

?

210. What is discount? The present worth of any sum of money How illustrated? -211. Are interest and discount the same? Explain the difference. Which is the greater, the interest or discount on any sum, for a given time? 212. What terms are given in discount, and what is required? To what do these correspond in interest?

Since the present worth of $ 1.06, due one year hence, at 6 per cent., is $ 1, the present worth of $ 25.44 is as many dollars as $1.06 is contained times in $ 25.44, or $ 24. We thus find the present worth to be $ 24, which, subtracted from the given sum, gives $ 1.44 as the discount.

-

RULE. Find the amount of $1 for the given time and rate; by which divide the given sum, and the quotient will be the PRESENT WORTH. The present worth subtracted from the given sum will give the DIS

COUNT.

NOTE.The discount may be found directly by making the interest of $1 for the given rate and time the numerator of a fraction, and the amount of $1 for the given rate and time the denominator, and then multiply the given sum by this fraction.

EXAMPLES FOR PRACTICE.

2. What is the present worth of $152.64, due 1 year hence?

Ans. $144.

3. What is the present worth of $ 477.71, due 4 years hence? Ans. $385.25.

4. What is the discount of $172.86, due 3 hence?

years, 4 months Ans. $28.81.

5. What is the discount of $800, due 3 years, 7 months, and 18 days hence? Ans. $143.186.

6. Samuel Heath has given his note for $375.75, dated Oct. 4, 1852, payable to John Smith, or order, Jan. 1, 1854; what is the real value of the note at the time given? Ans. $349.697.

7. Bought a chaise and harness of Isaac Morse for $125.75, for which I gave him my note, dated Oct. 5, 1852, to be paid in 6 months; what is the present value of the note, Jan. 1, 1853? Ans. $123.81.

213. Explain the operation for finding the present worth and discount. The reason of the operation? The rule? What other method is given?

COMMISSION, BROKERAGE, AND STOCKS.

214. Commission is the percentage paid to an agent, factor, or commission merchant, for buying or selling goods, or transacting other business.

Brokerage is the percentage paid to a dealer in money and stocks, called a broker, for making exchanges of money, negotiating different kinds of bills of credit, or transacting other like business.

Stocks is a general name given to government bonds, and to the money capital of corporations, such as banks, insurance, railroad, manufacturing, and mining companies.

Stocks are usually divided into equal shares, the market value of which is often variable.

When stocks sell for their original value they are said to be at par; when for more than their original value, above par, or at a premium; when for less than their original value, below par, or at a discount.

The premium, or advance, and the discount on stocks, are generally computed at a certain per cent. on the original value of the shares.

The rate per cent. of commission or brokerage is not regulated by law, but varies in different places, and with the nature of the business transacted.

Commission and brokerage are computed in the same manner. 215. To find the commission or brokerage on any sum.

Ex. 1. A commission merchant sells goods to the amount of $879; what is his commission at 3 per cent.? Ans. $26.37.

Since commission is a percentage on the given sum, the commission on $879, at 3 per cent., will be $879 .03 = $ 26.37.

RULE. - Find the percentage on the given sum cent., and the result is the commission or brokerage.

214. What is commission? Brokerage? Stock? divided? When are stocks at par? When above par? How is the premium or discount on stocks computed? and brokerage computed? -215. What is the rule?

at the given rate per (Art. 191.)

Into what are stocks

When below par? How are commission