IreTEREST, simple. If 51. is the interest of 100/. for a year, br .05, is the in terest of 11. for the same term: for, as 106 : 5 : : 1 : - Let then the interest 10' of IL for one year = the principal = p ; the time = t; the amount in the said time, viz principal and interest a.
Then r being the interest of IL for one year, the interest of 11. for two years will be 2 r; for three years, 3 r; and for any number of years, t r. Now, as one pound is to its interest, so is any given principal to its interest, or As 1 : tr ::p:p tr interest of p.
Then the principal being added to its in terest, their sum will be - a, the amount required ; which gives the following the orems for answering all questions relat ing to simple interest, viz.
If principal, time, and rate, are given, to find the amount.
Theo. 1.p t r--p--a.
If the amount, time, and rate, are giv en, to find the principal ? Theo. 2. --p.
tr4-1 If the principal, amount, and time, are given, to find the rate ? Theo. 3. a=1) pc .-- r.
If the principal, amount, and rate, are given, to find the time ? Theo. pr Ex. 1. What sum will one penny amount to in 1808 years, if put out to in terest at 5 per cent. per annum ? Multiply .004166 by 1808 and by .05, the product is .376666, which, add ed to the principal, gives .380833 75. 71d.
Ex. 2. What sum will amount to 1001.
in seven years, at 4 per cent. per annum ? Multiply 7 by .04, and add 1, which makes 1.28 ; divide 100/. by this sum, and the quotient is 78.125 = 78/. 2s. 6d.
Ex. 3. At what rate per cent. per an num, will 1001. amount to 145/. 108. in 7 years, at simple interest? Subtract 100/. from 145L 10s. the re mainder is 45/. 10s. which, divided by the product of the principal and time, or 700, gives .065 =‘% per cent.
Ex. 4. In what time will 125/. amount to 2121. 10s. at simple interest of 5 per cent. per annum ? Subtract 125L from 2121.10s. the re mainder is 871. 10s. which, divided by the product of the principal and rate, or 6.25, gives the answer,
14 years.
Tables of simple interest are easily computed, and many such have been pub lished, but those only are of much utility, which show readily the interest of any sum for any number of days. Such a ta ble is unavoidably very extensive, and forms of itself a thick volume; it cannot therefore be inserted in a work of this nature, but that which follows will answer all useful purposes to those who are ac quainted with decimal arithmetic. Such as prefer a table expressed in pounds, shillings, and pence, are referred to the interest tables published by Mr. John Thompson of Edinburgh, Mr. Joseph King of Liverpool, and particularly to the improved interest tables of Mr. William Reed, which show at one reference the interest at 5 per cent. of all sums, at the dates that usually occur in business.
The interest of any sum, for one day, is found by dividing the annual interest by 365; thus, at 5 per cent. the interest of 11. for one day is - - - - 00013699 which, multiplied by 2, gives the interest for 2 days - - 00027397 by 3 - - 3 - - - 00041096 by 4 - - 4 - - - 00054795 and by proceeding in this manner, the following table is easily formed.
Ex. 1. What is the interest of 2501. for 63 days ? .0086301 X 250 = 21. 3s. 14d.
The interest for any number of days, not specified in the table, may be easily found, by adding two of the numbers contained in it.
Ex. 2. What is the interest of 1151. for 237 days? The interest of 11. for 200 days is .0273972, and for 37 days .0050684, which added together make 0324656; therefore, .0324656 x 115 = 31. 14s. 8d. = the interest required.
By the act of 12 Anne, no person is to take for the loan of money, above 51. for the interest of 1001. for a year; and all notes, bonds, or other contracts made for money at a greater rate of interest, are to be void, and the offender to forfeit treble the value.