« ΠροηγούμενηΣυνέχεια »
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. . (Prample.
The interest of 450 lent at 5 per cent. per annum was
56 5s. ; how long was it lent 2
4. Principal, interest, and time given to find the rate ;
As given principal multiplied by the given time, is to 1 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. (Brample.
The interest of 250llent for 4 years is 50l, at what rate per cent. per annum was it lent 2 250 x 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 100l, so is the difference between the principal and amount, divided by the given time to the rate required. . . . . . :* . . . * * Gramipse. 500llent for 4 yrs amounted 600l, at what rate oct.was it lent? 500 : 100 : ... ++* : £5 the answer. 6. To find in what time any sum will amount to any number of times itself, at any rate per cent per annum ? Divide 1001 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. (trample. In what time will 350l amount to 3 times itself, at 6 per tent per annum, simple interest ?
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 percent. per an. will gain 150l? -
4. What principal lent on the first of May 1820, at 5 per cent. per annum, would amount to 500l, 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 1000l, at 5 per cent. per annum ?
6. In what time will 750l, amount to 9001, at 34 percent. per annum, simple interest?
7. How long must 1000l be lent at simple interest, to amount 1250l 10s, at 4% per cent, per annum ?
8. The interest of 1250l lent 219 days, is 371 10s. at what rate per cent was it lent?
9. What difference is there between the interest of 500l, at 6 per cent, per annum, and 250l 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 5000! 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 450l, at 5 per ct, per annum, simple interest, and at the expiration of a certain time, both ‘principal and interest amounted to 5601 10s. ; how long was it lent? * - r
12. At what rate per cent will the interest of 9001 for 3 years and 9 months amount to 1401?
13. At 5 per et, per annum, in what time will the interest of 425l amount to 5!? -
14. At 4% per cent. per annum, in what time will 100 amount to 100 guineas P
15. If a certain sum lent for 153 days, produce 61 10s. in terest, at 5 per cent. per anrum; what is the sum lent?
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 of 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 lace, the most usual charge is 2d, to pound of month, which s 10! # 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 100l due to me in three months hence, at 6 per cent per annum, the true discount will be ll 9s. 64d. which is the interest of 981 10s. 54d. for 3 months, and this ‘sum which I receive is the true present worth of 100l at the given rate and for the given time; but in real business I must allow ll 10s, which is the interest of 100l for three months. In this case, and all others where the time is short, as is ge'nerally 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 que, before it is o dué. Thus suppose a bill is drawn on the first of April, one month after 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, following..... Wi. a bili is drawn any number of mouths after date, calendar months are always understood. w
y 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. (Bramples. 1. Discounted a bill for 248l. 17s.6d. at 61 days at 4d. per pound sterling, what cash must be advanced for said bill? 36 s. d. 248-17 6 4d = or 4 2 114 Answer £244 14.6% 2. How much ready money must I pay for abill 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? laterest of 100l for 3 months, at 6 to ct. *an. is ll 10s.
- 2 4 4; . . . Answer £145 15 7# . . 6. What is the present worth of a bill of 78! 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 100l for 3 months, he would have at the rate of 6l is. It'd. Peo tent per annum ; if the time were 1 year he would have 6l 7s. 8+d. if? $. 61.16s. 4d. if 5 years 81 11s. 5d., if 10 years 15l. and if 15 years $0 per cent per annum. But where the time is long, as 2, 3, or inoré 3ears; a bill is seldom if ever discounted,
7, What is the present worth of a bill of 2151, drawn on
the 1st of March at 6 months, and discounted the 7th of June at 5 per cent per annum.? -
This bill will be due on the 4th of September, and from the 7th of June to this date the number of days is 89.
76540 product by 4 7,000)18,369,60 Till...., 215 0 0. 2,6242=2 12 53. Discount 2 12 5. Correction # Answer £212 7 7 £2 12 - 5
Find the present worths of the bills described under, at the given rates per cent per annum, and for the given times, each respectively. F. s. d drawn - time discounted rate 8, 234 6 8 4th of April at 3 mo, May 7th at 9. 270 17 6 5th of Febr. at 4 mo. March 10th at 10. 128 18 0 4th of March at 61 ds. April 11th at I 1. 427 13 4 7th of April at 41 ds. April 21st at 12. 343 12 6 15th of April at 61 ds. April 21st at 13. 108 10 0 1st of May at 91 ds. June 17th at 14. 714 16 0 10th of May at 4 mo, July 14th at 15. 594 18 Ü 21st of May at 6 mo. Aug. 21st at 16. 916 12 6 27th of May at 3 mo. Aug. 21st at 17. 174 15 0 1st of June at 91 ds, July 14th at-6 18. 1000 0 0 7th of June at 4 mo. Aug. 21st at 6 19. 815. 11 8 11th of June at 3 mo, July 21st at 5 20. 743 12 6 20th of June at 91 ds. July 21st at 6
CAsp 3d.—When several bills or sums at different times of
payment are to be discounted.
Multiply each amount by its time, until due, add the products together, and find the discount of their sum as before.