Solution. We find the discount on $300 is OPERATION. $1.50; and the discount on $300 at one per $300 cent. for 30 days is $0.25. Hence the required 298.50 rate is as many times 1 % as 25 is contained 1.50 discount. times in $1.50, which is 6%. 300 X.00145.25. 1.50 +25=6. Rule.—Divide the discount by the interest on the face, at 1% for the given time. WRITTEN EXERCISES. 2. Mr. Herr buys goods to the amount of $4000, and to pay for them gets his note for 60 days discounted at a bank; if the face is $4040.40, what is the rate ? Ans. 6%. 3. A note dated July 1st, 1875, at 3 months, was discounted at bank on Aug. 10, 1875; the face was $2500, and the proceeds $2474.722; what was the rate ? Ans. 7%. *4. A note dated September 12th, 1875, at 6 months, was discounted at Wilmington, Del., December 9th, 1875; the face of the note was $5750 and the proceeds $5624.77}; what was the rate of discount? Ans. 8%. STOCK INVESTMENTS WITH INTEREST. 309. In Stock Investments operators take into consideration the interest on the money invested. Since money is worth its interest while invested, to know the actual gain or loss of an investment, we should reckon the interest on the money invested. Stock speculators frequently, instead of paying for stock, deposit a sum called a "margin," to secure the broker against loss, should the stock fall in price before delivery or sale. NOTR.-As the following examples are worked principally by a combination of methods previously given, it has been thought unnecessary to divide them into cases. Brokerage at / per cent. is to be reckoned on :D purchases and sales. Money is considered worth 6%. 1. What is the annual rate of interest of an investment wbich pays 5% semi-annually, if reinvested at 6%? SOLUTION.-The dividend on $1 at the OPERATION. ond of the first 6 mo. is $.05, and this may $.05X1.03=$.0515 be on interest at 6% for the next 6 mo.; $.05+$.0515$.1015 hence at the end of the year this will 107%% amount to $.05X1.03, $.0515; and adding this to the second dividend on $1, which is received at the end of the second 6 mo., we have $.05+$.0515– 1015, which is the yearly rate of income. WRITTEN EXERCISES. 2. When the Penn. Railroad pays 2% quarterly, what yearly dividend will be equal to this? Ans. 88% 3. If I buy Michigan 6'8 at 108, interest payable semiannually, what annual rate % do I receive? Ans. 5731%. 4. If I buy 15.shares United Companies of New Jersey at 1374 ($100), and receive $374 dividend quarterly, what annial rate of interest do I receive? Ans. 733 %. SUPPLEMENTARY PROBLEMS. To be omitted unless otherwise directed. 6. Mr. Westlake sold $4000 Illinois 6's at 106, interest payable quarterly, and bought Kentucky 6's at 105, interest payable semiannually; did he increase or diminish his yearly income if each dividend was put out at interest as soon as recelved ? Ans. Diminished $1.80; surplus, $20. 6. I buy in August 20 shares Second and Third Sts. Pass. Railway ($50) at 83, and receive in October, January, April and July, a 3% dividend; what % income do I receive during the year, and what will be my entire dividend if each dividend is invested for the remainder of the year, at 8% interest ? Ans. Div. $123.60; rate, 744%. COMPOUND INTEREST. 510. Compound Interest is interest on both principal and interest, when the interest is not paid when due. Compound interest assumes that if the borrower does not pay the interest when due, it is proper that he should pay interest for it until paid. Some regard it as just, but it has not the sanction of law. 1. What is the compound interest of $400 for 2 yr, at 6%? OPERATION. SOLUTION.-Multiplying by the rate $400 per cent., we find the interest for 1 year .06 to be $24; adding this to the principal, 24.00=Int. 1st yr we find the amount to be $424, which is 400 the principal for the 2d year. Multiplying the new principal by the rate, 424.00=Amt. 1st yr. we find the interest for the 2d year to be .06 $25.44, and adding this to the 2d princi 25.44 Int. 2d T. pal, we find the amount for 2 years to 424 he $449.44, from which subtract the 1st principal, and the remainder, $49.44, is 449.44= Amt. 2d yr. 400 the compound interest. Hence the folloving 49.44=C. Int. for 2 yr. Rule.-I. Find the amount of the principal for the first period of time for which interest is reckoned, and make this the principal for the second period. II. Find the amount of this principal for the next period; and thus continue till the end of the given time. III. Subtract the given principal from the last amount, and the result will be the compound interest. Notes.-1. When the interest is due semi-annually or quarterly, we and the interest for such time and proceed as above directed. 2. When the time is for years, months, and days, find the amount for the years, then compute the interest on this for the months and dave, and add to the last amount before subtracting. WRITTEN EXERCISES. 2. What is the compound interest of $568, for 3 yr., at 6 per cent. ? Ans. $108.50. 3. What is the amount, at compound interest, of $90, for 6 yr., at 7 per cent. ? Ans. $135.061 4. What is the compound interest of $347.50, for 4 yr. 8 mo., at 6 per cent. ? Ans. $108.76. 5. What is the compound interest of $17281, for 2 yr. 6 mo., at 6 %, payable semi-annually ? Ans: $275.27. 6. What is the amount of $240, for 2 yr. 3 mo., at 8 per cent., payable quarterly ? Ans. $286.82. 7. What is the amount of $450, for 8 yr., at 6 per cent., compound interest ? SOLUTION.-We look in the table under 6 per cent., and opposite 8 yr. we find the amount of $1 to be $1.5938481 $1.5938481; multiplying this amount by 450, we 450 have the amount of $450, which is $717.23. $717.2302950 8. What is the amount of $780, for 9 yr., at 8 per cento, compound interest ? Ans. $1559.22. 9. What is the amount of $300, for 16 yr., at 7 per cent., compound interest ? Ans. $885.65. 10. Required the compound interest of $950, for 20 yr., at 4 per cent. Ans. $1131.57. 11. What is the difference between the simple and compound 10terest of $600 for 6 yr. 6 mo. 6 da. at 6% ?, Ans. $42.90, OPERATION. 511. The calculation of compound interest is facilitated by the use of the following table. Similar tables are also used for simple interest. TABLE. Amonnt of fi at Compound Interest in any number of years not exceeding 25. Yr. 2 per cent. 2% per cent. 3 per cent. 3% per cent. 4 per cent. 4% per cent. 1 3 5 6 9 IO 11 12 13 1.0200 0000 1.0250 0000 1.0300 0000 1,0350 0000 1.0400 0000 1.0450 0000 1.0404 0000 1.0506 2500 1,0609 0000 1.0712 2500 1.0816 0000 1.0920 2500 1.0612 0800 1.0768 9062 1.0927 2700 1.1087 1787 1.1248 6400 1.1411 6.12 1.0824 3216 1.1038 1289 1.1255 0881 1.1475 2300 1.1698 5856 1.1925 1860 1.1040 8080 1.1314 0821 1,1592 7407| 1.1876 8631 1.2166 5290 1.2461 8194 1,1261 6242 1,1596 9342 1.1940 5230 1.2292 55331 1.2653 1902 1.3022 6012 1,1486 8567) 1.1886 8575 1.2298 7387 1.2722 7926 1.3159 3178 1.3608 6183 1.1716 5938. 1.2184 0290 1.2667 7008 1.3168 0904 1.3685 6905 1.4221 oooi 1.1950 9257 1.2488 6297) 1.3047 7318 1.3628 9735 1.4233 1181 1.4860 9514 1,2189 9442 1.2800 8454 1.3439 1638 1.4105 9876 1.4802 4428 1.5529 6942 1.2433 7431 1.3120 8666 1.3842 3387 1.4599 6972 1.5394 5406 1.6228 5305 1,2682 4179 1.3448 8882 1.4257 6089 1.5110 6866 1.6010 3222 1.6958 8143 1.2936 0663 1.3785 1104 1.4685 3391 1.5639 5606 1.6650 7351 1.7721 9610 1.3194 7876 1.4129 7382 1.5125 8972 1.6186 9452) 2.7316 7645 1.3519 4492 1.3458 6834 1.4482 9817 1.5579 6742 1.6753 4883 1.8009 4351 1.9352 8244 1.3727 8570 1.4845 0562 2.6047 0644/ 1.7339 8604 1.8729 8125 2.0123 7015 1.4002 4142 1.5216 1826 1.6528 4763 1.7946 7555 1.9479 0050 3,1133 7681 1.4282 4625 1.5596 5872 1.7024 3306 1.8574 8920 2.0258 1652 2.2084 7877 1.4568 1117 1.5986 5019 1.7535 0605 1.9225 0132 2.1068 49181 2.3078 6031 1.4859 4740 1.6386 1644 1.8061 1123 1.9897 8886) 2.1911 2314 2.4117 1403 1.5156 6634 1.6795 8185 1.8602 9457 2.0594 3147 2.2787 6807 2.5202 4116 1.5459 7967 1.7215 7140 1.9161 0341 2.1315 1158 2.3699 1879 2.6336 5201 1.5768 9926 1.9646 1068 1.9735 8651 2,2061 1448 2.4647 1555 2.7521 7635 1.6084 3725 1.8087 2595 2.0327 9411 2.2833 2849 2.5633 0417 2.8760 1383 1,6406 0599 1.8539 4410 2.0931 1793 2,3632 4498 2.6658 3633 3.0054 3448 15 16 17 18 19 20 21 22 23 24 25 1 2 3 1.0600 000 1.0900 000 1.1910 160 1.4115 816 1.5386 240 1,1000 000 1,2100 000 1.3310 000 1.4641 000 1.6105 100 1.7715 610 1.9487 171 1.9925 626 2.1435 888 1.0500 000 1.1025 000 1.1576 250 1.2155 063 1.2762 816 1.3400 956 1.4071 004 1.4774 554 1.5513 282 1.6288 946 1.7103 394 1.7958 563 1,8856 491 1.9799 316 2.0789 282 2.1828 746 2.2920 183 2.4066 192 2.5269 502 2,6532 977 2.7859 626 2.9252 607 3.0715 238 3.2250 999 3.3863 549 1.2624 770 1.3382 256 1.4185 191 1.5036 303 1.9938 481 1.6894 790 1.7908 477 1.8982 986 2.0121 965 2,1329 283 2.2609 440 2.3965 582 2.5403 517 2.6927 728 2.8543 392 3.0255 995 3.2071 355 3.3995 636 3.60 35 374 3.8197 497 4.0489 346 4.2918 7071 1.0700 000 1.0800 000 1.4693 281 1.5868. 743 1.6057 815 1.7138 243 1.7181 862 1.8509 302 1.8384 592 1.9990 046 1.9671 514 2.1589 250 2.1048 520 2.3316 390 2.2521 916 2.5181 701 2.4098 450 2.7196 237 2.5785 342 2.9371 9361 2.7590 315 3.1721 691 2.9521 638 3.4259 426 3.1588 152 3.7000 181 3.3799 323 3.9960 195 3.6165 275 4.3157 011 3.8696 845 4.6609 571 4.1405 624 5.0338 337 4:4304 017 5.4365 404 4.7405 299 5.8714 637 5.0723 670 6.341 807 5.4274 326 5.8484 752 2.1718 933 2.3579 477 2.3673 637 2.5937 425 2.5804 264 2.8531 167 2,8126 648 3.1384 284 3.0658 046 3.4522 712 3.3417 270 3.7974 983 3.6424 825 4.1772 482 3.9703 059 4.5949 730 4.3276 334 5.0544 703 4.7171 204 5.5599 173 5.1416 613 6.1159 390 5.6044 108 6.7275 000 6.1088 077 7.4002 199 6.6586 004 8.1402 749 7.2578 745 8.9543 034 7.9110 8321 9.8497 329 8.6230 8071 10.8347 oso EXCHANGE. 512. Exchange is the method of making payments in distant places by means of Drafts or Bills of Exchange. 513. Exchange is of two kinds, Domestic and Foreign. Exchange between two places in the same country is called Domestic or Inland Exchange; that between different coun tries is called Foreign Exchange. 514. A Draft or Bill of Exchange is a written order for the payment of money. In domestic exchange a bill is usually called a Draft. 515. A Sight Bill is one payable "at sight" or on its presentation. A Time Bill is one payable at a specified time after sight or after date. 516. The Indorsement of a bill is the writing upon the back of it, by which the payee transfers the payment to another. A special indorsement is an order to pay the bill to some particular person, who is then called the Indorsee, and he alone can collect the bill. An indorsement in blank is the writing of the holder's name upon the back, which makes the bill payable to the bearer. The person who signs the bill is called the Maker or Drawer ; the person requested to pay is called the Drawee ; the person to whom the money is to be paid, is the Payee ; the person who has possession of the bill is called the Owner or Holder. 517. The Acceptance of a bill is the promise of the Drawee, when presented, to pay it at maturity. The Drawee accepts by writing across the face of the bill, “ Accepted," with the date and his signature; the bill is then called an Acceptance, and is of the character of a promissory note If a bill is protested for non-acceptance, the maker is under obligation to pay it immediately, although the time specified in it has not expired. Bills of exchange are entitled to “ days of grace" according to the custom of the place where the draft is payable. In New York, Pennsylvania, etc., no grace is allowed, and in most States no grace is allowed on sight drafts. If a note is payable on demand it is legally due when presented, as bank-notes, etc. |