SOLUTION.-Subtracting $594 from $600, we find the discount is $6. The discount on $1.00 for one day, at 6%, is of a mill; and on $600 it is 600×$.0001, or $0.10. Hence the note was discounted for as many days as $0.10 is contained times in $6, or 60 days. OPERATION. $600 594 6 discount. 600.000.10. 6.00.10-60 days. Rule.-Divide the discount by the interest on the face for one day. NOTE.-When grace is allowed, we subtract three days from the quotient to find the time of the note. WRITTEN EXERCISES. and 2. A merchant discounts a note for $2000 at a bank, receives $1970; what is the time? Ans. 90 days. 3. A commission merchant sold a consignment of cotton for $4500, receiving in payment a note, which yielded, on being discounted, $4477.50; what was the time of the note? Ans. 30 days. 4. A note dated June 21st, 1875, was discounted July 1st at 7%; the face of the note was $6540 and the proceeds $6472.60; how long had it to run after it was discounted? Ans. 53 days. SUPPLEMENTARY PROBLEMS. To be omitted unless otherwise directed. *5. A note dated Jan. 15th, 1884, at 6 months, was discounted at the First National Bank, St. Louis; the proceeds were $8402.25, aud the face $8500; what was the date of discount? Ans. May 11. 6. An interest-bearing note, dated Aug. 1, 1888, at 90 days, was discounted at 8%; the face was $750, and the proceeds $759.982; what was the date of discount? Ans. Sept. 30. CASE IV. 508. Given, the face, the time, and the proceeds or the discount, to find the rate. 1. The proceeds of a note for $300, at 30 days, are $298.50; what is the rate? SOLUTION.-We find the discount on $300 is $1.50; and the discount on $300 at one per cent. for 30 days is $0.25. Hence the required rate is as many times 1% as 25 is contained times in $1.50, which is 6%. Rule. OPERATION. $300 1.50 discount. 300X.00.25. 1.50÷25-6. 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 $5624.777; what was the rate of discount? Ans. 8%. STOCK INVESTMENTS WITH INTEREST. 509. 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. NOTE. 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 all purchases and sales. Money is considered worth 6%. 1. What is the annual rate of interest of an investment which pays 5% semi-annually, if reinvested at 6%? SOLUTION.-The dividend on $1 at the end of the first 6 mo. is $.05, and this may be on interest at 6% for the next 6 mo.; hence at the end of the year this will amount to $.05 1.03, $.0515; and adding this to the second dividend on $1, which OPERATION. $.05 1.03-$.0515 $.05+$.0515-$.1015 10,8% is received at the end of the second 6 mo., we have $.05+$.05151015, 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. 8%. 3. If I buy Michigan 6's at 108, interest payable semiannually, what annual rate % do I receive? Ans. 5211%. 4. If I buy 15 shares United at 137 ($100), and receive $37 annual rate of interest do I receive? Companies of New Jersey dividend quarterly, what Ans. 7%. SUPPLEMENTARY PROBLEMS. To be omitted unless otherwise directed. 5. 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, 7%. 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%? SOLUTION.-Multiplying by the rate per cent., we find the interest for 1 year to be $24; adding this to the principal, we find the amount to be $424, which is the principal for the 2d year. Multiplying the new principal by the rate, we find the interest for the 2d year to be $25.44, and adding this to the 2d principal, we find the amount for 2 years to be $449.44, from which subtract the 1st principal, and the remainder, $49.44, is the compound interest. Hence the following 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 days, 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. $135.06. 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; multiplying this amount by 450, we have the amount of $450, which is $717.23. OPERATION. $1.5938481 450 $717.2302950 8. What is the amount of $780, for 9 yr., at 8 per cent., 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. simple and com 11. What is the difference between the pound interest of $600 for 6 yr. 6 mo. 6 da. at 6%? Ans. $42.90. 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 §1 at Compound Interest in any number of years not exceeding 25. Yr. 2 per cent. 2% per cent. 3 per cent. 31⁄2 per cent. 4 per cent.4% per cent. |