CASE II. 506. Given, the rate, the time, and the proceeds or the discount, to find the face. 1. I wish to borrow $800 from a bank; for what must I give my note at 30 days, discounting at 6 per cent.? SOLUTION. We find the interest of $1 for 33 days and subtract it from $1, which gives the proceeds of $1. If for every $1 in the face of the note the proceeds are $0.9945, to give $800 proceeds will require as many times one dollar as $0.9945 is contained times in $800, which are $804.42. OPERATION. $1.0000 .9945, Proceeds of $1. =$804.42+. 800 .9945 Rule. Divide the given proceeds by the proceeds of $1 for the given time and rate; or divide the discount by the discount of $1. WRITTEN EXERCISES. 2. A wishes to borrow $1000 from a bank for 60 days; for what sum must be give his note, discounting at 6 per cent.? Ans. $1010.61. 3. What is the face of a note at 90 days, the proceeds of which, discounted at 6%, are $2000 ? Ans. $2031.50. at 60 days to net Ans. $5053.06. less than the face; Ans. $1904.76. when discounted Ans. $730.03. day note, which required the face Ans. $1040.31. days at a Balti 4. For what sum must a note be drawn $5000, when discounted at 6 per cent.? 5. A broker buys a 60 day note for $20 what was the face, discount 6 per cent.? 6. Find the face of a 6 mo. note which, at 1 per cent. a month, yields $685.50. 7. Mr. Brown, owing $1000, gave a 90 was discounted at 14 per cent. a month; of the note to pay the exact debt. 8. Mr. Schofield presented a note for 30 more bank for discount; the proceeds being $954.56, what was the face of the note? Ans $960. CASE III. 507. Given, the face, the rate, and the proceeds or the discount, to find the time. 1. The proceeds of a note for $600, discounted at 6%, arc $593.70; what was the time? SOLUTION.-Subtracting $593.70 from $600, we find the discount is $6.30. The discount on $1.00 for one day, at 6%, is of a mill; and on $600 it is 600×$.000, or $0.10. Hence the note was discounted for as many days as $0.10 is contained time in $6.30, or 63 days. Therefore, the time was 63-3, or 60 days. OPERATION. $600 6.30 discount. 600×.000/=.10 6.30.10=63 days. 63-3-60 days. Rule.- Divide the discount by the interest on the face for one day, and subtract 3 days of grace from the quotient. NOTE.-When the time a note has to run after being discounted is required, we wish to know the actual time, and therefore do not subtract the days of grace. WRITTEN EXERCISES. 2. A merchant discounts a note for $2000 at a bank, and receives $1969; 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, $4475.25; 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. 5. A note dated Jan. 15th, 1876, at 6 months, was discounted at the First National Bank, St. Louis; the proceeds were $8402.25, and the face $8500; what was the date of discount? Ans. May 11. 6. An interest-bearing note, dated Aug. 1, 1872, at 90 days was discounted at 8%; the face was $750, and the proceeds $759.982; what was the date of discount? Ans. Oct. 1. 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 $298.35; what is the rate? D SOLUTION. We find the discount on $300 is $1.65; and the discount on $300 at one per cent. for 33 days is $0.27. Hence the required rate is as many times 1% as 27 is contained times in $1.65, which is 6%. OPERATION. $300 1.65 discount. 300X.0027}. 1.65÷271=6. Rule.-Divide the discount by the interest on the face, a 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 $4042.45, 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 $2473.264; 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; wkat 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%? OPERATION. $.05 x 1.03=$.0515 $.05 $.0515= $.1015 SOLUTION.-The interest for the first half year may be on interest during the second half year at 6%; hence, at the end of the year the interest for the first half year will amount to $.05 x 1.03, or $.0515, which, added to the interest of the second half year, $.05, gives $.1015 as the yearly interest on $1. = 102% % WRITTEN EXERCISES. 2. When the Penn. Railroad pays 2% quarterly, what yearly dividend will be equal to this? Ans. 85%. 3. If I buy Michigan 6's at 108, interest payable semiannually, what annual rate % do I receive? Ans. 53%. 4. If I buy 15 shares United Companies of New Jersey at 137 ($100), and receive $37 dividend quarterly, what annual rate of interest do I receive? Ans. 733%. 551 5. Mr. Westlake sold $4000 Illinois 6's at 106, interest payable quarterly, and bought Kentucky 6's at 105, interest payable semi-annually; did he increase or diminish his yearly income if each dividend was put out at interest as soon as received? 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 % of 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, interest at 8%? Ans. Div., $123.60; rate, 7288%. COMPOUND INTEREST. 665 510. 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 Multithe principal for the 2d year. plying 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 find 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 $17284, for 2 yr. 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. |