102. Dr.....W. B. in account current with C. F... Cr. How much is due to W.B. for interest on the 21st of November, or is he overpaid interest, at 6 per cent. per annum? 103. Cr.... C.J. in account current with J.L. & Co........ Crs 1817. L d. 1817. L ́s. d. Sept. 3, To Cash 1175 18 6 Sept. 19, By Cash 1464 12 6 Dec. 21, To Cash 1818. 841 17 6 986 15 0 1818. Jan. 27, To Cash THE preceding cases illustrate the most useful applications of Interest: the following theorems contain all that is farther necessary on the subject ; 1. Interest, time, and rate, being given to find the principal. As the interest of 1001 for the given time is to the given interest, so is 1001 to the principal required. Example. The interest of a sum of money lent for 5 years, at five per cent. per annum is 457 10s. what sum is lent? 5 X 5 251 interest of 1001 for 5 years. 251 451 10s. : : 100: 182/ the answer. 2. Principal, time, and rate being given to find the amount. As 100 is to the given principal, so is 100 and its interest added thereto to the amount. Example. What will 4001 amount to in 4 years and 6 month, at 5 per cent. per annum? 5 X 4 100 : 400 = 2241 interest of 1001 for given time. ;; 122; 490/ the answer. 3. Principal, interest, and rate, being given to find the time. As the interest of the given principal for 1 year is to the given interest, so is one year to the time. Example. The interest of 4501 lent at 5 per cent. per annum wag 561 5s.; how long was it lent? 5 450 £22 10 interest for 1 year. As 22 10 56 5 1 year: 24 years Answer. . 4. Principal, interest, and time given to find the rate; As given principal multiplied by the given time, is to 100 multiplied by 1 year, or 12 months, or 365 days, according as the given time is years, months, or days, so is the given interest to the rate required. Example. The interest of 250/ lent for 4 years is 501, at what rate per cent. per annum was it lent? 250 × 4 = 1000 and 100 × 1= 120 1000 : 100 50 5 rate required. : 5. Principal, time and amount given to find the rate. As the given principal is to 100, so is the difference between the principal and amount, divided by the given time to the rate required. Example. 500/ lent for 4 yrs amounted 6007, at what rate ct.was it lent? 100: £5 the answer. 500: 100 6. To find in what time any sum will amount to any number of times itself, at any rate e per cent per annum? Divide 1007 by the rate per cent, and the quotient will give the time it would double itself, and this quotient multiplied by the number of times less 1, will produce the time required. NOTE. This is a particular case of Theofem 3d. Erample. In what time will 3501 amount to 3 times itself, at 6 per cent per annum, simple interest? 6)100 3-1= 2 Answer, 334 years: QUESTIONS FOR EXERCISE IN INTEREST. 1. How much money must be lent on the second of May at 5 per cent per annum to bring in for interest 15 on the 25th of December following? 2. What principal at 41 per cent. per annum, will bring a yearly income of 791 12s. 6d. ? 3. What principal lent from the first of January until the first of November in the following year, at 5 per cent. per an. will gain 150/? 4. What principal lent on the first of May 1820, at 5 per cent. per annum, would amount to 500, on the 4th of July in the same year? 5. What sum must be lent at simple interest, that the amount at the end of 3 years and 4 months may be 10001, at 5 per cent. per annum ? 6. In what time will 7501, amount to 9001, at 3 per cent. per annum, simple interest ? 7. How long must 1000/ be lent at simple interest, to amount 1250/ 10s. at 44 per cent. per annum ? 8. The interest of 1250/ lent 219 days, is 377 10s. at what rate per cent was it lent? 9. What difference is there between the interest of 5007, at 6 per cent. per annum, and 2501 at 3 per cent. per annum, the former lent for 2 and the latter for 4 years? 10. Suppose a minor, 18 years of age has a legacy of 50001 left him; what sum must his guardian pay him when he comes to the age of 21, allowing 6 per ct. per an. simple interest? 11. Suppose I lent at interest 4501, at 5 per ct. per annum, simple interest, and at the expiration of a certain time, both principal and interest amounted to 560/ 10s.; how long was it lent? 12. At what rate per cent will the interest of 9001 for 3 years and 9 months amount to 140/? 13. At 5 per ct. per annum, in what time will the interest of 4251 amount to 51? 14. At 4 per cent. per annum, in what time will 100! amount to 100 guineas ? 15. If a certain sum lent for 153 days, produce 67 10s. ins terest, at 5 per cent. per anrum; what is the sum lent? DISCOUNT. DISCOUNT is an allowance or consideration paid by the holder of a bill or note, on being advanced cash for it, before it becomes due or payable. The present worth of any sum or debt, due some time hence, is such a sum as if put to interest for that time, at a certain rate per cent per annum, would amount to the sum or debt. The present legal rate of interest being 6 per cent in Ireland, most discount transactions are calculated thereat, and bankers and merchants when discounting bills, find the interest of the sums for which they are drawn, from the time the bills are discounted to the time they become due, including days of grace, which they subtract as discount, and either pay or give credit for the balance. * It is not uncommon for this allowance to be made at so much pound; these latter transactions take place when tradesmen and others are in want of money, when they will pay a much greater discount than interest, which though the law does not sanction, yet the person accommodated seldom takes advantage of it. When such discount transactions take place, the most usual charge is 2d. pound & month, which is 101 cent annum. The true discount of any sum of money, due at a time to come, is the interest of such a sum, as if put to interest for the time the bill or note had to run, would, when added to its principal, amount to the sum for which said bill or note is drawn; thus if I have 1007 due to me in three months hence, at 6 per cent per annum, the true discount will be 11 9s. 6d. which is the interest of 981 10s. 54d. for 3 months, and this sum which I receive is the true present worth of 1001 at the given rate and for the given time; but in real business I must allow 11 10s. which is the interest of 1001 for three months. In this case, and all others where the time is short, as is generally the case with bills-discounted, the difference is so * In Great Britain and Ireland, 3 days called days of grace, are always allowed after the time the bill is nominally due, before it is legally due. Thus suppose a bill is drawn on the first of April, one month af ter date it would be payable on the fourth and not on the first of May, unless that day were Sunday, in which case a foreign bill would be payable on the day before, and a domestic bill on the day foliowing. When a bill is drawn any number of mouths after date, calendar months are always understood. trifling as not to require notice. If the time were long, the error would be considerable.* CASE 1st. To find the discount of any sum at any rate per pound sterling. Divide the given sum by the denominator of such aliquot part as this rate may be of a pound sterling. Examples. 1. Discounted á bill for 2481 17s. 6d. at 61 days at 4d. per pound sterling, what cash must be advanced for said bill? 2. How much ready money must I pay for a bill for 568! 12s. 6d. at 3 months date, deducting 6d. per pound discount? 3. What sum must be paid for a bill drawn for 2571 10s. at 41 days, at 3d. per pound sterling? 4. Bought goods amounting to 1473/ 6s. 8d. and am allowed 9d. per pound for ready money, how much money will pay for said goods? CASE 2d. To find the present worth of any sum, at any rate per cent. Find the interest of the debt, at the given rate and for the given time, which subtract from the debt? 5. Required the present worth of a bill for 1481, due at the end of 3 months, at 6 per cent per annum? Interest of 1001 for 3 months, at 6 ct. an. is 17 10s. 148 at 1/ 10s. Od. per cent. And 74 10= 100)222 2 4 44 Answer £145 15 74 6. What is the present worth of a bill of 781 15s. due on the first of August, but paid on the 5th of June preceding, at 6 per cent. per annum? *In every case where interest is subtracted as discount, the discounter has a greater rate of interest than the nominal rate, and the longer the time the greater is the rate; for recurring to the above example of 1001 for 3 months, he would have at the rate of 6 Is. 10d. per cent per annum; if the time were 1 year he would have 61 7s. 8d. if 2 years 67 16s. 44d. if 5 years 8/ 11s. 5d. if 10 years 157. and if 15 years 60 per cent per annum. But where the time is long, as 2, 3, or inore Years; a bill is seldom if ever discounted. |