132 60 2 233 61 3 4 435 63 5 536 64 6 7 8 637 65 839 67 91 121 152 182 213 244 274 305 335 98 128 159 189 220 251 281 312 342 The above Table will be useful in finding the number of days from any given day, to any other given day. Interest for days, months, and years. RULE 1st. The number of days from the beginning of the year to any given day of any month, may be obtained by inspection, thus from January the 1st. to June 24th. are 175 days. 2d. To find what is the number of days, from any given day of any month, to the end of the year. Suppose June 24th. then from 365 days. take the number answering to June 24th. ́175 190 Ans. 3d. To find the number of days between the given day of any month, and the given day of any other month, in the same year. How many days are there between June the 24th. and September the 29th? From the number answering to September 29th. 272 days. take that answering to June 24th. 175 97 Ans. 4th. To find the number of days from any given day of any month in one year, to any given day of any month in the next year. Find the number of days from September the 29th. in one ear, to June the 24th. in the next year? From the days of a year 365 days. take the number answering to September 29th. 272 days to the end of the year 33 175 268 Ans. Find the number of days from the beginning of the year to the 25th. of March, and from that day to the 24th. of June, and from that day to the 29th. September, and from that day to the end of the year, and find the interest of a bill of exchange for two thousand pounds for each given time, at 5 per cent. per annum ? March September 29 days 24 25th. 84 £23... 0... 91 = 97 = 24...18...74 73. rem. December 31 26...11...6 73' 20 73' Find the discount upon 12 bills of exchange of £100 each, from the beginning of the year to the end of it in 12 questions, discount being at 5 per cent. per annum, the 1st. bill being one month after date, the 2d. 2 months, the 3d. three months, &c. &c. each bill being one month longer than the preceding one? N. B. It is usual to allow what is termed 3 days grace, upon all bills of exchange, therefore 3 days interest should be added to every bill, (which is omitted in the above questions) which is 9 upon a bill of £100 for 12 months, or nearly 1d. per month upon each £100. If a bill be drawn 12 months after date for £100. a banker will charge for the discount £5...0...9. errors are frequently made in discounting bills which are dated on the following days, the 28th. February, 30th. of April, 30th. of June, 30th. of September and 30th. of November, if discount be calculated by the month. In the regular way of discounting bills, a very considerable profit is made, (more than 5 per cent. being always received) because no allowance of interest is made for the discount. A bill of £1000 at 12 months after date, for being discounted at 5 per cent. would cost £50, (without paying for the 3 days grace, which is only taken by bankers.) consequently the owner of the bill would receive only £950 in cash, which if put to interest for 12 months would produce £47.10.0+950=£997. 10.0+ loss by discounting £2. 10.0 £1000 the amount of the bill. Therefore, a gentleman who dis counts bills at 12 months after date gains part of the whole amount of the bills so discounted, if bills, at 9 months if at 6 months, if at 3 months to part, because he receives for his discount more than 5 per cent. per annum. Proof. He gives for the bill 9 £950. 0.0 Interest for one year for the above sum is 47.10.0 As discounts should be £999. 19.11.999999 1d. What will a banker gain (more than 5 per cent.) in one year, by Siscounting £10000, per day of each kind of bills at 12.9.6 and 3 months? Ans. 12 months £5325. 9 months £2995.6.3. 5.0. 3 months £332.16.3. 6 months £133: Hence it is evident that a banker gains more by discounting long dated bill, than he does by short dated ones. ALGEB R A. DEFINITIONS. ALGEBRA is the art of computing by symbols. 1. Like quantities are those which consist of the same letters. 2. Unlike quantities are those which consist of different letters. 3. Given quantities are those whose values are known. 4. Unknown quantities are those whose values are unknown. 5. Simple quantities are those which consist of one term only. 6. Compound quantities are those which consist of several terms. 7. Positive or affirmative quantities are those which are to be added. 8. Negative quantities are those which are to be subtracted. 9. Like signs are all affirmative (+), or all negative (→). 10. Unlike signs are when some are affirmative (+), and others negative (-). 11. The co-efficient of any quantity, is the number prefixed to it. 12. A binomial quantity is one consisting of two terms; a trinomial of three terms; a quadrinomial of four, &c. 13. A residual quantity is a binomial where one of the terms is negative. 14. The power of a quantity is its square, cube, biquadrate, &c. 15. The index or exponent of a quantity is the number which denotes its root or power. 16. A surd or irrational quantity is that which has no exact root. 17. A rational quantity is that which has no radical sign (√), or index annexed to it. 18. The reciprocal of any quantity is that quantity inverted, or unity divided by it. |